Starting from rest, a DVD steadily accelerates to 500 rpm

How do objects accelerate in two dimensions?

What is projectile motion?

What is relative motion?

What is circular motion?

What is centripetal acceleration?

Where is two-dimensional motion used?

A sports cars position on a winding road is given by r u = 16.0t - 0.10t 2 + 0.00048t 3 2ni + 18.0t + 0.060t 2 - 0.00095t 3 2nj where the y-axis points north, t is in s, and r is in m. What are the cars speed and direction at t = 120 s?

During which time interval or intervals is the particle described by these position graphs at rest? More than one may be correct. a. 01 s b. 12 s c. 23 s d. 34 s

A ball rolls down a long hill, through the valley, and back up the other side. Draw a complete motion diagram of the ball.

This acceleration will cause the particle to a. Speed up and curve upward. c. Slow down and curve upward. e. Move to the right and down. b. Speed up and curve downward. d. Slow down and curve downward. f. Reverse direction.

In the distant future, a small spacecraft is drifting north through the galaxy at 680 m/s when it receives a command to return to the starship. The pilot rotates the spacecraft until the nose is pointed 25 north of east, then engages the ion engine. The spacecraft accelerates at 75 m/s2 . Plot the spacecrafts trajectory for the first 20 s.

A 50 g marble rolls off a table and hits 2 m from the base of the table. A 100 g marble rolls off the same table with the same speed. It lands at distance a. Less than 1 m. b. 1 m. c. Between 1 m and 2 m. d. 2 m. e. Between 2 m and 4 m. f. 4 m.

A stunt man drives a car off a 10.0-m-high cliff at a speed of 20.0 m/s. How far does the car land from the base of the cliff?

A plane traveling horizontally to the right at 100 m/s flies past a helicopter that is going straight up at 20 m/s. From the helicopters perspective, the planes direction and speed are a. Right and up, less than 100 m/s. b. Right and up, 100 m/s. c. Right and up, more than 100 m/s. d. Right and down, less than 100 m/s. e. Right and down, 100 m/s. f. Right and down, more than 100 m/s

Frogs, with their long, strong legs, are excellent jumpers. And thanks to the good folks of Calaveras County, California, who have a jumping frog contest every year in honor of a Mark Twain story, we have very good data on how far a determined frog can jump. High-speed cameras show that a good jumper goes into a crouch, then rapidly extends his legs by typically 15 cm during a 65 ms push off, leaving the ground at a 30 angle. How far does this frog leap?

A particle moves cw around a circle at constant speed for 2.0 s. It then reverses direction and moves ccw at half the original speed until it has traveled through the same angle. Which is the particles angle-versus-time graph?

The police are chasing a bank robber. While driving at 50 m/s, they fire a bullet to shoot out a tire of his car. The police gun shoots bullets at 300 m/s. What is the bullets speed as measured by a TV camera crew parked beside the road?

Rank in order, from largest to smallest, the centripetal accelerations aa to ae of particles a to e. r (a) v 2r (d) v 2r (e)

Cleveland is 300 miles east of Chicago. A plane leaves Chicago flying due east at 500 mph. The pilot forgot to check the weather and doesnt know that the wind is blowing to the south at 50 mph. What is the planes ground speed? Where is the plane 0.60 h later, when the pilot expects to land in Cleveland?

The fan blade is slowing down. What are the signs of v and a? a. v is positive and a is positive. b. v is positive and a is negative. c. v is negative and a is positive. d. v is negative and a is negative.

A wiser pilot flying from Chicago to Cleveland on the same day plots a course that will take her directly to Cleveland. In which direction does she fly the plane? How long does it take to reach Cleveland?

A 4.0-cm-diameter crankshaft turns at 2400 rpm (revolutions per minute). What is the speed of a point on the surface of the crankshaft?

FIGURE 4.25 shows the angular position of a painted dot on the edge of a rotating wheel. Describe the wheels motion and draw an v@versus@t graph.

A small steel roulette ball rolls ccw around the inside of a 30-cmdiameter roulette wheel. The ball completes 2.0 rev in 1.20 s. a. What is the balls angular velocity? b. What is the balls position at t = 2.0 s? Assume ui = 0.

A typical carnival Ferris wheel has a radius of 9.0 m and rotates 4.0 times per minute. What speed and acceleration do the riders experience?

FIGURE 4.31a is a graph of angular velocity versus time for a rotating wheel. Describe the motion and draw a graph of angular acceleration versus time

A ceiling fan spinning at 60 rpm coasts to a stop 25 s after being turned off. How many revolutions does it make while stopping?

Youve been assigned the task of measuring the start-up characteristics of a large industrial motor. After several seconds, when the motor has reached full speed, you know that the angular acceleration will be zero, but you hypothesize that the angular acceleration may be constant during the first couple of seconds as the motor speed increases. To find out, you attach a shaft encoder to the 3.0-cm-diameter axle. A shaft encoder is a device that converts the angular position of a shaft or axle to a signal that can be read by a computer. After setting the computer program to read four values a second, you start the motor and acquire the following data: Time (s) Angle () Time (s) Angle () 0.00 0 1.00 267 0.25 16 1.25 428 0.50 69 1.50 620 0.75 161 a. Do the data support your hypothesis of a constant angular acceleration? If so, what is the angular acceleration? If not, is the angular acceleration increasing or decreasing with time? b. A 76-cm-diameter blade is attached to the motor shaft. At what time does the acceleration of the tip of the blade reach 10 m/s2 ?

One day when you come into lab, you see a spring-loaded wheel that can launch a ball straight up. To do so, you place the ball in a cup on the rim of the wheel, turn the wheel to stretch the spring, then release. The wheel rotates through an angle u, then hits a stop when the cup is level with the axle and pointing straight up. The cup stops, but the ball flies out and keeps going. Youre told that the wheel has been designed to have constant angular acceleration as it rotates through u. The lab assignment is first to measure the wheels angular acceleration. Then the lab instructor is going to place a target at height h above the point where the ball is launched. Your task will be to launch the ball so that it just barely hits the target. a. Find an expression in terms of quantities that you can measure for the angle u that launches the ball at the correct speed. b. Evaluate u if the wheels diameter is 62 cm, youve determined that its angular acceleration is 200 rad/s2 , the mass of the ball is 25 g, and the instructor places the target 190 cm above the launch point.

a. At this instant, is the particle in FIGURE Q4.1 speeding up, slowing down, or traveling at constant speed? b. Is this particle curving to the right, curving to the left, or traveling straight?

a. At this instant, is the particle in FIGURE Q4.2 speeding up, slowing down, or traveling at constant speed? b. Is this particle curving upward, curving downward, or traveling straight?

Tarzan swings through the jungle by hanging from a vine. a. Immediately after stepping off a branch to swing over to another tree, is Tarzans acceleration a u zero or not zero? If not zero, which way does it point? Explain. b. Answer the same question at the lowest point in Tarzans swing.

A projectile is launched at an angle of 30. a. Is there any point on the trajectory where v u and a u are parallel to each other? If so, where? b. Is there any point where v u and a u are perpendicular to each other? If so, where?

For a projectile, which of the following quantities are constant during the flight: x, y, r, vx, vy, v, ax, ay? Which of these quantities are zero throughout the flight?

A cart that is rolling at constant velocity on a level table fires a ball straight up. a. When the ball comes back down, will it land in front of the launching tube, behind the launching tube, or directly in the tube? Explain. b. Will your answer change if the cart is accelerating in the forward direction? If so, how?

A rock is thrown from a bridge at an angle 30 below horizontal. Immediately after the rock is released, is the magnitude of its acceleration greater than, less than, or equal to g? Explain

Anita is running to the right at 5 m/s in FIGURE Q4.8. Balls 1 and 2 are thrown toward her by friends standing on the ground. According to Anita, both balls are approaching her at 10 m/s.Which ball was thrown at a faster speed? Or were they thrown with the same speed? Explain.

An electromagnet on the ceiling of an airplane holds a steel ball. When a button is pushed, the magnet releases the ball. The experiment is first done while the plane is parked on the ground, and the point where the ball hits the floor is marked with an X. Then the experiment is repeated while the plane is flying level at a steady 500 mph. Does the ball land slightly in front of the X (toward the nose of the plane), on the X, or slightly behind the X (toward the tail of the plane)? Explain.

Zack is driving past his house in FIGURE Q4.10. He wants to toss his physics book out the window and have it land in his driveway. If he lets go of the book exactly as he passes the end of the driveway, should he direct his throw outward and toward the front of the car (throw 1), straight outward (throw 2), or outward and toward the back of the car (throw 3)? Explain.

In FIGURE Q4.11, Yvette and Zack are driving down the freeway side by side with their windows down. Zack wants to toss his physics book out the window and have it land in Yvettes front seat. Ignoring air resistance, should he direct his throw outward and toward the front of the car (throw 1), straight outward (throw 2), or outward and toward the back of the car (throw 3)? Explain.

In uniform circular motion, which of the following quantities are constant: speed, instantaneous velocity, the tangential component of velocity, the radial component of acceleration, the tangential component of acceleration? Which of these quantities are zero throughout the motion?

FIGURE Q4.13 shows three points on a steadily rotating wheel. a. Rank in order, from largest to smallest, the angular velocities v1, v2, and v3 of these points. Explain. b. Rank in order, from largest to smallest, the speeds v1, v2, and v3 of these points. Explain.

FIGURE Q4.14 shows four rotating wheels. For each, determine the signs 1+ or -2 of v and a.

FIGURE Q4.15 shows a pendulum at one end point of its arc. a. At this point, is v positive, negative, or zero? Explain. b. At this point, is a positive, negative, or zero? Explain.

Problems 1 and 2 show a partial motion diagram. For each: a. Complete the motion diagram by adding acceleration vectors. b. Write a physics problem for which this is the correct motion diagram. Be imaginative! Dont forget to include enough information to make the problem complete and to state clearly what is to be found.Answer Problems 3 through 5 by choosing one of the eight labeled acceleration vectors or selecting option I: a u = 0 u .

Problems 1 and 2 show a partial motion diagram. For each: a. Complete the motion diagram by adding acceleration vectors. b. Write a physics problem for which this is the correct motion diagram. Be imaginative! Dont forget to include enough information to make the problem complete and to state clearly what is to be found.Answer Problems 3 through 5 by choosing one of the eight labeled acceleration vectors or selecting option I: a u = 0 u .

At this instant, the particle has steady speed and is curving to the right. What is the direction of its acceleration?

At this instant, the particle is speeding up and curving upward. What is the direction of its acceleration?

At this instant, the particle is speeding up and curving downward. What is the direction of its acceleration?

A rocket-powered hockey puck moves on a horizontal frictionless table. FIGURE EX4.6 shows graphs of vx and vy, the x- and y-components of the pucks velocity. The puck starts at the origin. a. In which direction is the puck moving at t = 2 s? Give your answer as an angle from the x-axis. b. How far from the origin is the puck at t = 5 s?

A rocket-powered hockey puck moves on a horizontal frictionless table. FIGURE EX4.7 shows graphs of vx and vy, the x- and y-components of the pucks velocity. The puck starts at the origin. What is the magnitude of the pucks acceleration at t = 5 s?

A particles trajectory is described by x = 1 1 2 t 3 - 2t 2 2m and y = 1 1 2 t 2 - 2t2m, where t is in s. a. What are the particles position and speed at t = 0 s and t = 4 s? b. What is the particles direction of motion, measured as an angle from the x-axis, at t = 0 s and t = 4 s?

A particle moving in the xy-plane has velocity v u = 12tni + 13 - t 2 2nj2 m/s, where t is in s. What is the particles acceleration vector at t = 4 s? 10. || You have a remote-controlled car that has been programmed to have velocity v u = 1-3tni + 2t 2 nj2 m/s, where t is in s. At t = 0 s, the car is at r u 0 = 13.0ni + 2.0nj2 m. What are the cars (a) position vector and (b) acceleration vector at t = 2.0 s?

A ball thrown horizontally at 25 m/s travels a horizontal distance of 50 m before hitting the ground. From what height was the ball thrown?

A physics student on Planet Exidor throws a ball, and it follows the parabolic trajectory shown in FIGURE EX4.12. The balls position is shown at 1 s intervals until t = 3 s. At t = 1 s, the balls velocity is v u = 12.0 ni + 2.0 nj2 m/s. a. Determine the balls velocity at t = 0 s, 2 s, and 3 s. b. What is the value of g on Planet Exidor? c. What was the balls launch angle?

A supply plane needs to drop a package of food to scientists working on a glacier in Greenland. The plane flies 100 m above the glacier at a speed of 150 m/s. How far short of the target should it drop the package?

A rifle is aimed horizontally at a target 50 m away. The bullet hits the target 2.0 cm below the aim point. a. What was the bullets flight time? b. What was the bullets speed as it left the barrel?

In the Olympic shotput event, an athlete throws the shot with an initial speed of 12.0 m/s at a 40.0 angle from the horizontal. The shot leaves her hand at a height of 1.80 m above the ground. How far does the shot travel?

On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a 6 iron. The free-fall acceleration on the moon is 1/6 of its value on earth. Suppose he hit the ball with a speed of 25 m/s at an angle 30 above the horizontal. a. How much farther did the ball travel on the moon than it would have on earth? b. For how much more time was the ball in flight?

A baseball player friend of yours wants to determine his pitching speed. You have him stand on a ledge and throw the ball horizontally from an elevation 4.0 m above the ground. The ball lands 25 m away. What is his pitching speed?

A boat takes 3.0 hours to travel 30 km down a river, then 5.0 hours to return. How fast is the river flowing?

When the moving sidewalk at the airport is broken, as it often seems to be, it takes you 50 s to walk from your gate to baggage claim. When it is working and you stand on the moving sidewalk the entire way, without walking, it takes 75 s to travel the same distance. How long will it take you to travel from the gate to baggage claim if you walk while riding on the moving sidewalk?

Mary needs to row her boat across a 100-m-wide river that is flowing to the east at a speed of 1.0 m/s. Mary can row with a speed of 2.0 m/s. a. If Mary points her boat due north, how far from her intended landing spot will she be when she reaches the opposite shore? b. What is her speed with respect to the shore?

A kayaker needs to paddle north across a 100-m-wide harbor. The tide is going out, creating a tidal current that flows to the east at 2.0 m/s. The kayaker can paddle with a speed of 3.0 m/s. a. In which direction should he paddle in order to travel straight across the harbor? b. How long will it take him to cross?

Susan, driving north at 60 mph, and Trent, driving east at 45 mph, are approaching an intersection. What is Trents speed relative to Susans reference frame?

| FIGURE EX4.23 shows the angular-velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4 s?

FIGURE EX4.24 shows the angular-position-versus-time graph for a particle moving in a circle. What is the particles angular velocity at (a) t = 1 s, (b) t = 4 s, and (c) t = 7 s?

FIGURE EX4.25 shows the angular-velocity-versus-time graph for a particle moving in a circle, starting from u0 = 0 rad at t = 0 s. Draw the angular-position-versus-time graph. Include an appropriate scale on both axes.

The earths radius is about 4000 miles. Kampala, the capital of Uganda, and Singapore are both nearly on the equator. The distance between them is 5000 miles. The flight from Kampala to Singapore takes 9.0 hours. What is the planes angular velocity with respect to the earths surface? Give your answer in /h.

An old-fashioned single-play vinyl record rotates on a turntable at 45 rpm. What are (a) the angular velocity in rad/s and (b) the period of the motion?

As the earth rotates, what is the speed of (a) a physics student in Miami, Florida, at latitude 26, and (b) a physics student in Fairbanks, Alaska, at latitude 65? Ignore the revolution of the earth around the sun. The radius of the earth is 6400 km

How fast must a plane fly along the earths equator so that the sun stands still relative to the passengers? In which direction must the plane fly, east to west or west to east? Give your answer in both km/h and mph. The earths radius is 6400 km.

A 3000-m-high mountain is located on the equator. How much faster does a climber on top of the mountain move than a surfer at a nearby beach? The earths radius is 6400 km.

Peregrine falcons are known for their maneuvering ability. In a tight circular turn, a falcon can attain a centripetal acceleration 1.5 times the free-fall acceleration. What is the radius of the turn if the falcon is flying at 25 m/s?

To withstand g-forces of up to 10 gs, caused by suddenly pulling out of a steep dive, fighter jet pilots train on a human centrifuge. 10 gs is an acceleration of 98 m/s2 . If the length of the centrifuge arm is 12 m, at what speed is the rider moving when she experiences 10 gs?

The radius of the earths very nearly circular orbit around the sun is 1.5 * 1011 m. Find the magnitude of the earths (a) velocity, (b) angular velocity, and (c) centripetal acceleration as it travels around the sun. Assume a year of 365 days

A speck of dust on a spinning DVD has a centripetal acceleration of 20 m/s2 . a. What is the acceleration of a different speck of dust that is twice as far from the center of the disk? b. What would be the acceleration of the first speck of dust if the disks angular velocity was doubled?

Your roommate is working on his bicycle and has the bike upside down. He spins the 60-cm-diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. What are the pebbles speed and acceleration?

FIGURE EX4.36 shows the angular velocity graph of the crankshaft in a car. What is the crankshafts angular acceleration at (a) t = 1 s, (b) t = 3 s, and (c) t = 5 s?

FIGURE EX4.37 shows the angular acceleration graph of a turntable that starts from rest. What is the turntables angular velocity at (a) t = 1 s, (b) t = 2 s, and (c) t = 3 s?

FIGURE EX4.38 shows the angular-velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4 s?

A wheel initially rotating at 60 rpm experiences the angular acceleration shown in FIGURE EX4.39. What is the wheels angular velocity, in rpm, at t = 3.0 s?

A 5.0-m-diameter merry-go-round is initially turning with a 4.0 s period. It slows down and stops in 20 s. a. Before slowing, what is the speed of a child on the rim? b. How many revolutions does the merry-go-round make as it stops?

An electric fan goes from rest to 1800 rpm in 4.0 s. What is its angular acceleration?

A bicycle wheel is rotating at 50 rpm when the cyclist begins to pedal harder, giving the wheel a constant angular acceleration of 0.50 rad/s2 . a. What is the wheels angular velocity, in rpm, 10 s later? b. How many revolutions does the wheel make during this time?

Starting from rest, a DVD steadily accelerates to 500 rpm in 1.0 s, rotates at this angular speed for 3.0 s, then steadily decelerates to a halt in 2.0 s. How many revolutions does it make?

A spaceship maneuvering near Planet Zeta is located at r u = 1600ni - 400nj + 200k n2 * 103 km, relative to the planet, and traveling at v u = 9500ni m/s. It turns on its thruster engine and accelerates with a u = 140ni - 20k n2 m/s2 for 35 min. What is the spaceships position when the engine shuts off? Give your answer as a position vector measured in km.

A particle moving in the xy-plane has velocity v u 0 = v0xni + v0ynj at t = 0. It undergoes acceleration a u = btni - cvynj, where b and c are constants. Find an expression for the particles velocity at a later time t

A projectiles horizontal range over level ground is v0 2 sin 2u/g. At what launch angle or angles will the projectile land at half of its maximum possible range?

a. A projectile is launched with speed v0 and angle u. Derive an expression for the projectiles maximum height h. b. A baseball is hit with a speed of 33.6 m/s. Calculate its height and the distance traveled if it is hit at angles of 30.0, 45.0, and 60.0

A projectile is launched from ground level at angle u and speed v0 into a headwind that causes a constant horizontal acceleration of magnitude a opposite the direction of motion. a. Find an expression in terms of a and g for the launch angle that gives maximum range. b. What is the angle for maximum range if a is 10% of g?

A gray kangaroo can bound across level ground with each jump carrying it 10 m from the takeoff point. Typically the kangaroo leaves the ground at a 20 angle. If this is so: a. What is its takeoff speed? b. What is its maximum height above the ground?

A ball is thrown toward a cliff of height h with a speed of 30 m/s and an angle of 60 above horizontal. It lands on the edge of the cliff 4.0 s later. a. How high is the cliff? b. What was the maximum height of the ball? c. What is the balls impact speed?

A tennis player hits a ball 2.0 m above the ground. The ball leaves his racquet with a speed of 20.0 m/s at an angle 5.0 above the horizontal. The horizontal distance to the net is 7.0 m, and the net is 1.0 m high. Does the ball clear the net? If so, by how much? If not, by how much does it miss?

You are target shooting using a toy gun that fires a small ball at a speed of 15 m/s. When the gun is fired at an angle of 30 above horizontal, the ball hits the bulls-eye of a target at the same height as the gun. Then the target distance is halved. At what angle must you aim the gun to hit the bulls-eye in its new position? (Mathematically there are two solutions to this problem; the physically reasonable answer is the smaller of the two.)

A 35 g steel ball is held by a ceiling-mounted electromagnet 3.5 m above the floor. A compressed-air cannon sits on the floor, 4.0 m to one side of the point directly under the ball. When a button is pressed, the ball drops and, simultaneously, the cannon fires a 25 g plastic ball. The two balls collide 1.0 m above the floor. What was the launch speed of the plastic ball?

You are watching an archery tournament when you start wondering how fast an arrow is shot from the bow. Remembering your physics, you ask one of the archers to shoot an arrow parallel to the ground. You find the arrow stuck in the ground 60 m away, making a 3.0 angle with the ground. How fast was the arrow shot?

Youre 6.0 m from one wall of the house seen in FIGURE P4.55. You want to toss a ball to your friend who is 6.0 m from the opposite wall. The throw and catch each occur 1.0 m above the ground. a. What minimum speed will allow the ball to clear the roof? b. At what angle should you toss the ball?

Sand moves without slipping at 6.0 m/s down a conveyer that is tilted at 15. The sand enters a pipe 3.0 m below the end of the conveyer belt, as shown in FIGURE P4.56. What is the horizontal distance d between the conveyer belt and the pipe?

A stunt man drives a car at a speed of 20 m/s off a 30-m-high cliff. The road leading to the cliff is inclined upward at an angle of 20. a. How far from the base of the cliff does the car land? b. What is the cars impact speed?

A javelin thrower standing at rest holds the center of the javelin behind her head, then accelerates it through a distance of 70 cm as she throws. She releases the javelin 2.0 m above the ground traveling at an angle of 30 above the horizontal. Top-rated javelin throwers do throw at about a 30 angle, not the 45 you might have expected, because the biomechanics of the arm allow them to throw the javelin much faster at 30 than they would be able to at 45. In this throw, the javelin hits the ground 62 m away. What was the acceleration of the javelin during the throw? Assume that it has a constant acceleration

A rubber ball is dropped onto a ramp that is tilted at 20, as shown in FIGURE P4.59. A bouncing ball obeys the law of reflection, which says that the ball leaves the surface at the same angle it approached the surface. The balls next bounce is 3.0 m to thright of its first bounce. What is the balls rebound speed on its first bounce?

You are asked to consult for the citys research hospital, where a group of doctors is investigating the bombardment of cancer tumors with high-energy ions. As FIGURE P4.60 shows, ions are fired directly toward the center of the tumor at speeds of 5.0 * 106 m/s. To cover the entire tumor area, the ions are deflected sideways by passing them between two charged metal plates that accelerate the ions perpendicular to the direction of their initial motion. The acceleration region is 5.0 cm long, and the ends of the acceleration plates are 1.5 m from the target. What sideways acceleration is required to deflect an ion 2.0 cm to one side?

Ships A and B leave port together. For the next two hours, ship A travels at 20 mph in a direction 30 west of north while ship B travels 20 east of north at 25 mph. a. What is the distance between the two ships two hours after they depart? b. What is the speed of ship A as seen by ship B?

While driving north at 25 m/s during a rainstorm you notice that the rain makes an angle of 38 with the vertical. While driving back home moments later at the same speed but in the opposite direction, you see that the rain is falling straight down. From these observations, determine the speed and angle of the raindrops relative to the ground.

Youve been assigned the task of using a shaft encodera device that measures the angle of a shaft or axle and provides a signal to a computerto analyze the rotation of an engine crankshaft under certain conditions. The table lists the crankshafts angles over a 0.6 s interval. Time (s) Angle (rad) 0.0 0.0 0.1 2.0 0.2 3.2 0.3 4.3 0.4 5.3 0.5 6.1 0.6 7.0 Is the crankshaft rotating with uniform circular motion? If so, what is its angular velocity in rpm? If not, is the angular acceleration positive or negative?

A circular track has several concentric rings where people can run at their leisure. Phil runs on the outermost track with radius rP while Annie runs on an inner track with radius rA = 0.80rP. The runners start side by side, along a radial line, and run at the same speed in a counterclockwise direction. How many revolutions has Annie made when Annies and Phils velocity vectors point in opposite directions for the first time?

A typical laboratory centrifuge rotates at 4000 rpm. Test tubes have to be placed into a centrifuge very carefully because of the very large accelerations. a. What is the acceleration at the end of a test tube that is 10 cm from the axis of rotation? b. For comparison, what is the magnitude of the acceleration a test tube would experience if dropped from a height of 1.0 m and stopped in a 1.0-ms-long encounter with a hard floor?

Astronauts use a centrifuge to simulate the acceleration of a rocket launch. The centrifuge takes 30 s to speed up from rest to its top speed of 1 rotation every 1.3 s. The astronaut is strapped into a seat 6.0 m from the axis. a. What is the astronauts tangential acceleration during the first 30 s? b. How many gs of acceleration does the astronaut experience when the device is rotating at top speed? Each 9.8 m/s2 of acceleration is 1 g

Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The radius of the earth is 6.37 * 106 m, and the altitude of a geosynchronous orbit is 3.58 * 107 m 122,000 miles2. What are (a) the speed and (b) the magnitude of the acceleration of a satellite in a geosynchronous orbit?

A computer hard disk 8.0 cm in diameter is initially at rest. A small dot is painted on the edge of the disk. The disk accelerates at 600 rad/s2 for 1 2 s, then coasts at a steady angular velocity for another 1 2 s. a. What is the speed of the dot at t = 1.0 s? b. Through how many revolutions has the disk turned?

A high-speed drill rotating ccw at 2400 rpm comes to a halt in 2.5 s. a. What is the magnitude of the drills angular acceleration? b. How many revolutions does it make as it stops?

A turbine is spinning at 3800 rpm. Friction in the bearings is so low that it takes 10 min to coast to a stop. How many revolutions does the turbine make while stopping?

Your 64-cm-diameter car tire is rotating at 3.5 rev/s when suddenly you press down hard on the accelerator. After traveling 200 m, the tires rotation has increased to 6.0 rev/s. What was the tires angular acceleration? Give your answer in rad/s2 .

The angular velocity of a process control motor is v = 120 - 1 2 t 2 2rad/s, where t is in seconds. a. At what time does the motor reverse direction? b. Through what angle does the motor turn between t = 0 s and the instant at which it reverses direction?

A Ferris wheel of radius R speeds up with angular acceleration a starting from rest. Find an expression for the (a) velocity and (b) centripetal acceleration of a rider after the Ferris wheel has rotated through angle u

A 6.0-cm-diameter gear rotates with angular velocity v = 12.0 + 1 2 t 2 2 rad/s, where t is in seconds. At t = 4.0 s, what are: a. The gears angular acceleration? b. The tangential acceleration of a tooth on the gear?

A painted tooth on a spinning gear has angular acceleration a = 120 - t2 rad/s2 , where t is in s. Its initial angular velocity, at t = 0 s, is 300 rpm. What is the tooths angular velocity in rpm at t = 20 s?

A car starts from rest on a curve with a radius of 120 m and accelerates tangentially at 1.0 m/s2 . Through what angle will the car have traveled when the magnitude of its total acceleration is 2.0 m/s2 ?

A long string is wrapped around a 6.0-cm-diameter cylinder, initially at rest, that is free to rotate on an axle. The string is then pulled with a constant acceleration of 1.5 m/s2 until 1.0 m of string has been unwound. If the string unwinds without slipping, what is the cylinders angular speed, in rpm, at this time?

In Problems 78 through 80 you are given the equations that are used to solve a problem. For each of these, you are to a. Write a realistic problem for which these are the correct equations. Be sure that the answer your problem requests is consistent with the equations given. b. Finish the solution of the problem, including a pictorial representation.100 m = 0 m + 150 cos u m/s)t1 0 m = 0 m + 150 sin u m/s2t1 - 1 2 19.80 m/s2 2t1 2

vx = -16.0 cos 452 m/s + 3.0 m/s vy = 16.0 sin 452 m/s + 0 m/s 100 m = vyt1, x1 = vxt1

2.5 rad = 0 rad + vi110 s2 + 111.5 m/s2 2/2150 m22110 s22 vf = vi + 111.5 m/s2 2/150 m22110 s2

In one contest at the county fair, seen in FIGURE CP4.81, a spring-loaded plunger launches a ball at a speed of 3.0 m/s from one corner of a smooth, flat board that is tilted up at a 20 angle. To win, you must make the ball hit a small target at the adjacent corner, 2.50 m away. At what angle u should you tilt the ball launcher?

An archer standing on a 15 slope shoots an arrow 20 above the horizontal, as shown in FIGURE CP4.82. How far down the slope does the arrow hit if it is shot with a speed of 50 m/s from 1.75 m above the ground?

A skateboarder starts up a 1.0-m-high, 30 ramp at a speed of 7.0 m/s. The skateboard wheels roll without friction. At the top she leaves the ramp and sails through the air. How far from the end of the ramp does the skateboarder touch down?

A cannon on a train car fires a projectile to the right with speed v0, relative to the train, from a barrel elevated at angle u. The cannon fires just as the train, which had been cruising to the right along a level track with speed vtrain, begins to accelerate with acceleration a, which can be either positive (speeding up) or negative (slowing down). Find an expression for the angle at which the projectile should be fired so that it lands as far as possible from the cannon. You can ignore the small height of the cannon above the track.

A child in danger of drowning in a river is being carried downstream by a current that flows uniformly with a speed of 2.0 m/s. The child is 200 m from the shore and 1500 m upstream of the boat dock from which the rescue team sets out. If their boat speed is 8.0 m/s with respect to the water, at what angle from the shore should the pilot leave the shore to go directly to the child?