Determine the moment of inertia of the solid steel

Determine the moment of inertia Iy for the slender rod. The rods density r and cross-sectional area A are constant. Express the result in terms of the rods total mass m.

The solid cylinder has an outer radius R, height h, and is made from a material having a density that varies from its center as r = k + ar 2, where k and a are constants. Determine the mass of the cylinder and its moment of inertia about the z axis. R h z

Determine the moment of inertia of the thin ring about the z axis. The ring has a mass m.

The paraboloid is formed by revolving the shaded area around the x axis. Determine the radius of gyration kx. The density of the material is r = 5 Mg>m3 .

Determine the radius of gyration kx of the body. The specific weight of the material is g = 380 lb>ft3 .

The sphere is formed by revolving the shaded area around the x axis. Determine the moment of inertia Ix and express the result in terms of the total mass m of the sphere. The material has a constant density r.

The frustum is formed by rotating the shaded area around the x axis. Determine the moment of inertia Ix and express the result in terms of the total mass m of the frustum. The frustum has a constant density r.

The hemisphere is formed by rotating the shaded area around the y axis. Determine the moment of inertia Iy and express the result in terms of the total mass m of the hemisphere. The material has a constant density r

The hemisphere is formed by rotating the shaded area around the y axis. Determine the moment of inertia Iy and express the result in terms of the total mass m of the hemisphere. The material has a constant density r

The pendulum consists of a 4-kg circular plate and a 2-kg slender rod. Determine the radius of gyration of the pendulum about an axis perpendicular to the page and passing through point O.

The assembly is made of the slender rods that have a mass per unit length of 3 kg>m. Determine the mass moment of inertia of the assembly about an axis perpendicular to the page and passing through point O.

Determine the moment of inertia of the solid steel assembly about the x axis. Steel has a specific weight of gst = 490 lb>ft3 .

The wheel consists of a thin ring having a mass of 10 kg and four spokes made from slender rods and each having a mass of 2 kg. Determine the wheels moment of inertia about an axis perpendicular to the page and passing through point A

If the large ring, small ring and each of the spokes weigh 100 lb, 15 lb, and 20 lb, respectively, determine the mass moment of inertia of the wheel about an axis perpendicular to the page and passing through point A.

Determine the moment of inertia about an axis perpendicular to the page and passing through the pin at O. The thin plate has a hole in its center. Its thickness is 50 mm, and the material has a density r = 50 kg>m3 .

Determine the mass moment of inertia of the thin plate about an axis perpendicular to the page and passing through point O. The material has a mass per unit area of 20 kg>m2 .

Determine the location y of the center of mass G of the assembly and then calculate the moment of inertia about an axis perpendicular to the page and passing through G. The block has a mass of 3 kg and the semicylinder has a mass of 5 kg

Determine the moment of inertia of the assembly about an axis perpendicular to the page and passing through point O. The block has a mass of 3 kg, and the semicylinder has a mass of 5 kg

Determine the moment of inertia of the wheel about an axis which is perpendicular to the page and passes through the center of mass G. The material has a specific weight g = 90 lb>ft3 .

Determine the moment of inertia of the wheel about an axis which is perpendicular to the page and passes through point O. The material has a specific weight g = 90 lb>ft3

The pendulum consists of the 3-kg slender rod and the 5-kg thin plate. Determine the location y of the center of mass G of the pendulum; then calculate the moment of inertia of the pendulum about an axis perpendicular to the page and passing through G.

Determine the moment of inertia of the overhung crank about the x axis. The material is steel having a density of r = 7.85 Mg>m3 .

Determine the moment of inertia of the overhung crank about the x axis. The material is steel having a density of r = 7.85 Mg>m3 .

The door has a weight of 200 lb and a center of gravity at G. Determine how far the door moves in 2 s, starting from rest, if a man pushes on it at C with a horizontal force F = 30 lb. Also, find the vertical reactions at the rollers A and B.

The door has a weight of 200 lb and a center of gravity at G. Determine the constant force F that must be applied to the door to push it open 12 ft to the right in 5 s, starting from rest. Also, find the vertical reactions at the rollers A and B

The jet aircraft has a total mass of 22 Mg and a center of mass at G. Initially at take-off the engines provide a thrust 2T = 4 kN and T = 1.5 kN. Determine the acceleration of the plane and the normal reactions on the nose wheel at A and each of the two wing wheels located at B. Neglect the mass of the wheels and, due to low velocity, neglect any lift caused by the wings.

The sports car has a weight of 4500 lb and center of gravity at G. If it starts from rest it causes the rear wheels to slip as it accelerates. Determine how long it takes for it to reach a speed of 10 ft>s. Also, what are the normal reactions at each of the four wheels on the road? The coefficients of static and kinetic friction at the road are ms = 0.5 and mk = 0.3, respectively. Neglect the mass of the wheels

The assembly has a mass of 8 Mg and is hoisted using the boom and pulley system. If the winch at B draws in the cable with an acceleration of 2 m>s2, determine the compressive force in the hydraulic cylinder needed to support the boom. The boom has a mass of 2 Mg and mass center at G.

The assembly has a mass of 4 Mg and is hoisted using the winch at B. Determine the greatest acceleration of the assembly so that the compressive force in the hydraulic cylinder supporting the boom does not exceed 180 kN. What is the tension in the supporting cable? The boom has a mass of 2 Mg and mass center at G.

The uniform girder AB has a mass of 8 Mg. Determine the internal axial, shear, and bending-moment loadings at the center of the girder if a crane gives it an upward acceleration of 3 m>s2.

A car having a weight of 4000 lb begins to skid and turn with the brakes applied to all four wheels. If the coefficient of kinetic friction between the wheels and the road is mk = 0.8, determine the maximum critical height h of the center of gravity G such that the car does not overturn. Tipping will begin to occur after the car rotates 90 from its original direction of motion and, as shown in the figure, undergoes translation while skidding. Hint: Draw a free-body diagram of the car viewed from the front. When tipping occurs, the normal reactions of the wheels on the right side (or passenger side) are zero.

A force of P = 300 N is applied to the 60-kg cart. Determine the reactions at both the wheels at A and both the wheels at B. Also, what is the acceleration of the cart? The mass center of the cart is at G.

Determine the largest force P that can be applied to the 60-kg cart, without causing one of the wheel reactions, either at A or at B, to be zero. Also, what is the acceleration of the cart? The mass center of the cart is at G.

The trailer with its load has a mass of 150-kg and a center of mass at G. If it is subjected to a horizontal force of P = 600 N, determine the trailers acceleration and the normal force on the pair of wheels at A and at B. The wheels are free to roll and have negligible mass

The desk has a weight of 75 lb and a center of gravity at G. Determine its initial acceleration if a man pushes on it with a force F = 60 lb. The coefficient of kinetic friction at A and B is mk = 0.2.

The desk has a weight of 75 lb and a center of gravity at G. Determine the initial acceleration of a desk when the man applies enough force F to overcome the static friction at A and B. Also, find the vertical reactions on each of the two legs at A and at B. The coefficients of static and kinetic friction at A and B are ms = 0.5 and mk = 0.2, respectively

The 150-kg uniform crate rests on the 10-kg cart. Determine the maximum force P that can be applied to the handle without causing the crate to tip on the cart. Slipping does not occur.

The 150-kg uniform crate rests on the 10-kg cart. Determine the maximum force P that can be applied to the handle without causing the crate to slip or tip on the cart. The coefficient of static friction between the crate and cart is ms = 0.2

The bar has a weight per length w and is supported by the smooth collar. If it is released from rest, determine the internal normal force, shear force, and bending moment in the bar as a function of x

The smooth 180-lb pipe has a length of 20 ft and a negligible diameter. It is carried on a truck as shown. Determine the maximum acceleration which the truck can have without causing the normal reaction at A to be zero. Also determine the horizontal and vertical components of force which the truck exerts on the pipe at B.

The smooth 180-lb pipe has a length of 20 ft and a negligible diameter. It is carried on a truck as shown. If the truck accelerates at a = 5 ft>s 2 , determine the normal reaction at A and the horizontal and vertical components of force which the truck exerts on the pipe at B.

The uniform crate has a mass of 50 kg and rests on the cart having an inclined surface. Determine the smallest acceleration that will cause the crate either to tip or slip relative to the cart. What is the magnitude of this acceleration? The coefficient of static friction between the crate and cart is ms = 0.5.

Determine the acceleration of the 150-lb cabinet and the normal reaction under the legs A and B if P = 35 lb. The coefficients of static and kinetic friction between the cabinet and the plane are ms = 0.2 and mk = 0.15, respectively. The cabinets center of gravity is located at G.

The uniform bar of mass m is pin connected to the collar, which slides along the smooth horizontal rod. If the collar is given a constant acceleration of a, determine the bar's inclination angle u. Neglect the collar's mass.

The drop gate at the end of the trailer has a mass of 1.25 Mg and mass center at G. If it is supported by the cable AB and hinge at C, determine the tension in the cable when the truck begins to accelerate at 5 m>s2. Also, what are the horizontal and vertical components of reaction at the hinge C?

The drop gate at the end of the trailer has a mass of 1.25 Mg and mass center at G. If it is supported by the cable AB and hinge at C, determine the maximum deceleration of the truck so that the gate does not begin to rotate forward. What are the horizontal and vertical components of reaction at the hinge C?

The snowmobile has a weight of 250 lb, centered at G1, while the rider has a weight of 150 lb, centered at G2. If the acceleration is a = 20 ft>s 2 , determine the maximum height h of G2 of the rider so that the snowmobiles front skid does not lift off the ground. Also, what are the traction (horizontal) force and normal reaction under the rear tracks at A?

The snowmobile has a weight of 250 lb, centered at G1, while the rider has a weight of 150 lb, centered at G2. If h = 3 ft, determine the snowmobiles maximum permissible acceleration a so that its front skid does not lift off the ground. Also, find the traction (horizontal) force and the normal reaction under the rear tracks at A.

If the carts mass is 30 kg and it is subjected to a horizontal force of P = 90 N, determine the tension in cord AB and the horizontal and vertical components of reaction on end C of the uniform 15-kg rod BC

If the carts mass is 30 kg, determine the horizontal force P that should be applied to the cart so that the cord AB just becomes slack. The uniform rod BC has a mass of 15 kg

The pipe has a mass of 800 kg and is being towed behind the truck. If the acceleration of the truck is at = 0.5 m>s 2 , determine the angle u and the tension in the cable. The coefficient of kinetic friction between the pipe and the ground is mk = 0.1.

The pipe has a mass of 800 kg and is being towed behind a truck. If the angle u = 30, determine the acceleration of the truck and the tension in the cable. The coefficient of kinetic friction between the pipe and the ground is mk = 0.1.

The crate C has a weight of 150 lb and rests on the truck elevator for which the coefficient of static friction is ms = 0.4. Determine the largest initial angular acceleration a, starting from rest, which the parallel links AB and DE can have without causing the crate to slip. No tipping occurs.

The crate C has a weight of 150 lb and rests on the truck elevator. Determine the initial friction and normal force of the elevator on the crate if the parallel links are given an angular acceleration a = 2 rad>s 2 starting from rest.

The 100-kg uniform crate C rests on the elevator floor where the coefficient of static friction is ms = 0.4. Determine the largest initial angular acceleration a, starting from rest at u = 90, without causing the crate to slip. No tipping occurs.

The two uniform 4-kg bars DC and EF are fixed (welded) together at E. Determine the normal force NE, shear force VE, and moment ME, which DC exerts on EF at E if at the instant u = 60 BC has an angular velocity v = 2 rad>s and an angular acceleration a = 4 rad>s 2 as shown

The 10-kg wheel has a radius of gyration kA = 200 mm. If the wheel is subjected to a moment M = (5t) N # m, where t is in seconds, determine its angular velocity when t = 3 s starting from rest. Also, compute the reactions which the fixed pin A exerts on the wheel during the motion.

The uniform 24-kg plate is released from rest at the position shown. Determine its initial angular acceleration and the horizontal and vertical reactions at the pin A.

The uniform slender rod has a mass m. If it is released from rest when u = 0, determine the magnitude of the reactive force exerted on it by pin B when u = 90.

The bent rod has a mass of 2 kg>m. If it is released from rest in the position shown, determine its initial angular acceleration and the horizontal and vertical components of reaction at A.

If a horizontal force of P = 100 N is applied to the 300-kg reel of cable, determine its initial angular acceleration. The reel rests on rollers at A and B and has a radius of gyration of kO = 0.6 m.

The 10-lb bar is pinned at its center O and connected to a torsional spring. The spring has a stiffness k = 5 lb # ft>rad, so that the torque developed is M = (5u) lb # ft, where u is in radians. If the bar is released from rest when it is vertical at u = 90, determine its angular velocity at the instant u = 0.

The 10-lb bar is pinned at its center O and connected to a torsional spring. The spring has a stiffness k = 5 lb # ft>rad, so that the torque developed is M = (5u) lb # ft, where u is in radians. If the bar is released from rest when it is vertical at u = 90, determine its angular velocity at the instant u = 45.

A cord is wrapped around the outer surface of the 8-kg disk. If a force of F = (u2) N, where u is in radians, is applied to the cord, determine the disks angular acceleration when it has turned 5 revolutions. The disk has an initial angular velocity of v0 = 1 rad>s.

Disk A has a weight of 5 lb and disk B has a weight of 10 lb. If no slipping occurs between them, determine the couple moment M which must be applied to disk A to give it an angular acceleration of 4 rad>s2.

The kinetic diagram representing the general rotational motion of a rigid body about a fixed axis passing through O is shown in the figure. Show that IGA may be eliminated by moving the vectors m(aG)t and m(aG)n to point P, located a distance rGP = k2 G>rOG from the center of mass G of the body. Here kG represents the radius of gyration of the body about an axis passing through G. The point P is called the center of percussion of the body.

If the cord at B suddenly fails, determine the horizontal and vertical components of the initial reaction at the pin A, and the angular acceleration of the 120-kg beam. Treat the beam as a uniform slender rod.

The device acts as a pop-up barrier to prevent the passage of a vehicle. It consists of a 100-kg steel plate AC and a 200-kg counterweight solid concrete block located as shown. Determine the moment of inertia of the plate and block about the hinged axis through A. Neglect the mass of the supporting arms AB. Also, determine the initial angular acceleration of the assembly when it is released from rest at u = 45.

The 20-kg roll of paper has a radius of gyration kA = 90 mm about an axis passing through point A. It is pin supported at both ends by two brackets AB. If the roll rests against a wall for which the coefficient of kinetic friction is k = 0.2 and a vertical force F = 30 N is applied to the end of the paper, determine the angular acceleration of the roll as the paper unrolls.

The 20-kg roll of paper has a radius of gyration kA = 90 mm about an axis passing through point A. It is pin supported at both ends by two brackets AB. If the roll rests against a wall for which the coefficient of kinetic friction is k = 0.2, determine the constant vertical force F that must be applied to the roll to pull off 1 m of paper in t = 3 s starting from rest. Neglect the mass of paper that is removed.

The reel of cable has a mass of 400 kg and a radius of gyration of kA = 0.75 m. Determine its angular velocity when t = 2 s, starting from rest, if the force P = (20t 2 + 80) N, when t is in seconds. Neglect the mass of the unwound cable, and assume it is always at a radius of 0.5 m.

The 30-kg disk is originally spinning at v = 125 rad>s. If it is placed on the ground, for which the coefficient of kinetic friction is C = 0.5, determine the time required for the motion to stop. What are the horizontal and vertical components of force which the member AB exerts on the pin at A during this time? Neglect the mass of AB.

Cable is unwound from a spool supported on small rollers at A and B by exerting a force T = 300 N on the cable. Compute the time needed to unravel 5 m of cable from the spool if the spool and cable have a total mass of 600 kg and a radius of gyration of kO = 1.2 m. For the calculation, neglect the mass of the cable being unwound and the mass of the rollers at A and B. The rollers turn with no friction

The 5-kg cylinder is initially at rest when it is placed in contact with the wall B and the rotor at A. If the rotor always maintains a constant clockwise angular velocity v = 6 rad>s, determine the initial angular acceleration of the cylinder. The coefficient of kinetic friction at the contacting surfaces B and C is mk = 0.2.

The wheel has a mass of 25 kg and a radius of gyration kB = 0.15 m. It is originally spinning at v = 40 rad>s. If it is placed on the ground, for which the coefficient of kinetic friction is mC = 0.5, determine the time required for the motion to stop. What are the horizontal and vertical components of reaction which the pin at A exerts on AB during this time? Neglect the mass of AB.

The 20-kg roll of paper has a radius of gyration kA = 120 mm about an axis passing through point A. It is pin supported at both ends by two brackets AB. The roll rests on the floor, for which the coefficient of kinetic friction is k = 0.2. If a horizontal force F = 60 N is applied to the end of the paper, determine the initial angular acceleration of the roll as the paper unrolls.

Disk D turns with a constant clockwise angular velocity of 30 rad>s. Disk E has a weight of 60 lb and is initially at rest when it is brought into contact with D. Determine the time required for disk E to attain the same angular velocity as disk D. The coefficient of kinetic friction between the two disks is k = 0.3. Neglect the weight of bar BC.

Two cylinders A and B, having a weight of 10 lb and 5 lb, respectively, are attached to the ends of a cord which passes over a 3-lb pulley (disk). If the cylinders are released from rest, determine their speed in t = 0.5 s. The cord does not slip on the pulley. Neglect the mass of the cord. Suggestion: Analyze the system consisting of both the cylinders and the pulley

The two blocks A and B have a mass of 5 kg and 10 kg, respectively. If the pulley can be treated as a disk of mass 3 kg and radius 0.15 m, determine the acceleration of block A. Neglect the mass of the cord and any slipping on the pulley

The two blocks A and B have a mass mA and mB, respectively, where mB 7 mA. If the pulley can be treated as a disk of mass M, determine the acceleration of block A. Neglect the mass of the cord and any slipping on the pulley

Determine the angular acceleration of the 25-kg diving board and the horizontal and vertical components of reaction at the pin A the instant the man jumps off. Assume that the board is uniform and rigid, and that at the instant he jumps off the spring is compressed a maximum amount of 200 mm, v = 0, and the board is horizontal. Take k = 7 kN>m.

The lightweight turbine consists of a rotor which is powered from a torque applied at its center. At the instant the rotor is horizontal it has an angular velocity of 15 rad>s and a clockwise angular acceleration of 8 rad>s 2 . Determine the internal normal force, shear force, and moment at a section through A. Assume the rotor is a 50-m-long slender rod, having a mass of 3 kg>m.

The two-bar assembly is released from rest in the position shown. Determine the initial bending moment at the fixed joint B. Each bar has a mass m and length l.

The armature (slender rod) AB has a mass of 0.2 kg and can pivot about the pin at A. Movement is controlled by the electromagnet E, which exerts a horizontal attractive force on the armature at B of FB = (0.2(10-3 )l -2 ) N, where l in meters is the gap between the armature and the magnet at any instant. If the armature lies in the horizontal plane, and is originally at rest, determine the speed of the contact at B the instant l = 0.01 m. Originally l = 0.02 m

The bar has a weight per length of w. If it is rotating in the vertical plane at a constant rate v about point O, determine the internal normal force, shear force, and moment as a function of x and u.

The 4-kg slender rod is initially supported horizontally by a spring at B and pin at A. Determine the angular acceleration of the rod and the acceleration of the rods mass center at the instant the 100-N force is applied.

The 100-kg pendulum has a center of mass at G and a radius of gyration about G of kG = 250 mm. Determine the horizontal and vertical components of reaction on the beam by the pin A and the normal reaction of the roller B at the instant u = 90 when the pendulum is rotating at v = 8 rad>s. Neglect the weight of the beam and the support.

The 100-kg pendulum has a center of mass at G and a radius of gyration about G of kG = 250 mm. Determine the horizontal and vertical components of reaction on the beam by the pin A and the normal reaction of the roller B at the instant u = 0 when the pendulum is rotating at v = 4 rad>s. Neglect the weight of the beam and the support.

The Catherine wheel is a firework that consists of a coiled tube of powder which is pinned at its center. If the powder burns at a constant rate of 20 g>s such as that the exhaust gases always exert a force having a constant magnitude of 0.3 N, directed tangent to the wheel, determine the angular velocity of the wheel when 75% of the mass is burned off. Initially, the wheel is at rest and has a mass of 100 g and a radius of r = 75 mm. For the calculation, consider the wheel to always be a thin disk.

If the disk in Fig. 1719 rolls without slipping, show that when moments are summed about the instantaneous center of zero velocity, IC, it is possible to use the moment equation MIC = IIC a, where IIC represents the moment of inertia of the disk calculated about the instantaneous axis of zero velocity

The 20-kg punching bag has a radius of gyration about its center of mass G of kG = 0.4 m. If it is initially at rest and is subjected to a horizontal force F = 30 N, determine the initial angular acceleration of the bag and the tension in the supporting cable AB.

The uniform 150-lb beam is initially at rest when the forces are applied to the cables. Determine the magnitude of the acceleration of the mass center and the angular acceleration of the beam at this instant.

The slender 12-kg bar has a clockwise angular velocity of v = 2 rad>s when it is in the position shown. Determine its angular acceleration and the normal reactions of the smooth surface A and B at this instant.

The tire has a weight of 30 lb and a radius of gyration of kG = 0.6 ft. If the coefficients of static and kinetic friction between the tire and the plane are ms = 0.2 and mk = 0.15, determine the tires angular acceleration as it rolls down the incline. Set u = 12

The tire has a weight of 30 lb and a radius of gyration of kG = 0.6 ft. If the coefficients of static and kinetic friction between the tire and the plane are ms = 0.2 and mk = 0.15, determine the maximum angle u of the inclined plane so that the tire rolls without slipping

The spool has a mass of 100 kg and a radius of gyration of kG = 0.3 m. If the coefficients of static and kinetic friction at A are ms = 0.2 and mk = 0.15, respectively, determine the angular acceleration of the spool if P = 50 N

Solve Prob. 1796 if the cord and force P = 50 N are directed vertically upwards

The spool has a mass of 100 kg and a radius of gyration kG = 0.3 m. If the coefficients of static and kinetic friction at A are ms = 0.2 and mk = 0.15, respectively, determine the angular acceleration of the spool if P = 600 N.

The 12-kg uniform bar is supported by a roller at A. If a horizontal force of F = 80 N is applied to the roller, determine the acceleration of the center of the roller at the instant the force is applied. Neglect the weight and the size of the roller

. A force of F = 10 N is applied to the 10-kg ring as shown. If slipping does not occur, determine the rings initial angular acceleration, and the acceleration of its mass center, G. Neglect the thickness of the ring

If the coefficient of static friction at C is s = 0.3, determine the largest force F that can be applied to the 5-kg ring, without causing it to slip. Neglect the thickness of the ring

The 25-lb slender rod has a length of 6 ft. Using a collar of negligible mass, its end A is confined to move along the smooth circular bar of radius 322 ft. End B rests on the floor, for which the coefficient of kinetic friction is mB = 0.4. If the bar is released from rest when u = 30, determine the angular acceleration of the bar at this instant.

The 15-lb circular plate is suspended from a pin at A. If the pin is connected to a track which is given an acceleration aA = 5 ft>s2, determine the horizontal and vertical components of reaction at A and the angular acceleration of the plate. The plate is originally at rest.

If P = 30 lb, determine the angular acceleration of the 50-lb roller. Assume the roller to be a uniform cylinder and that no slipping occurs.

If the coefficient of static friction between the 50-lb roller and the ground is ms = 0.25, determine the maximum force P that can be applied to the handle, so that roller rolls on the ground without slipping. Also, find the angular acceleration of the roller. Assume the roller to be a uniform cylinder.

The uniform bar of mass m and length L is balanced in the vertical position when the horizontal force P is applied to the roller at A. Determine the bars initial angular acceleration and the acceleration of its top point B.

Solve Prob. 17106 if the roller is removed and the coefficient of kinetic friction at the ground is k.

The semicircular disk having a mass of 10 kg is rotating at v = 4 rad>s at the instant u = 60. If the coefficient of static friction at A is ms = 0.5, determine if the disk slips at this instant.

The 500-kg concrete culvert has a mean radius of 0.5 m. If the truck has an acceleration of 3m>s 2 , determine the culverts angular acceleration. Assume that the culvert does not slip on the truck bed, and neglect its thickness.

The 15-lb disk rests on the 5-lb plate. A cord is wrapped around the periphery of the disk and attached to the wall at B. If a torque M = 40 lb # ft is applied to the disk, determine the angular acceleration of the disk and the time needed for the end C of the plate to travel 3 ft and strike the wall. Assume the disk does not slip on the plate and the plate rests on the surface at D having a coefficient of kinetic friction of k = 0.2. Neglect the mass of the cord

The semicircular disk having a mass of 10 kg is rotating at v = 4 rad>s at the instant u = 60. If the coefficient of static friction at A is ms = 0.5, determine if the disk slips at this instant.

The circular concrete culvert rolls with an angular velocity of v = 0.5 rad>s when the man is at the position shown. At this instant the center of gravity of the culvert and the man is located at point G, and the radius of gyration about G is kG = 3.5 ft. Determine the angular acceleration of the culvert. The combined weight of the culvert and the man is 500 lb. Assume that the culvert rolls without slipping, and the man does not move within the culvert.

The uniform disk of mass m is rotating with an angular velocity of v0 when it is placed on the floor. Determine the initial angular acceleration of the disk and the acceleration of its mass center. The coefficient of kinetic friction between the disk and the floor is k.

The uniform disk of mass m is rotating with an angular velocity of v0 when it is placed on the floor. Determine the time before it starts to roll without slipping. What is the angular velocity of the disk at this instant? The coefficient of kinetic friction between the disk and the floor is k

A cord is wrapped around each of the two 10-kg disks. If they are released from rest determine the angular acceleration of each disk and the tension in the cord C. Neglect the mass of the cord.

The disk of mass m and radius r rolls without slipping on the circular path. Determine the normal force which the path exerts on the disk and the disks angular acceleration if at the instant shown the disk has an angular velocity of V.

The uniform beam has a weight W. If it is originally at rest while being supported at A and B by cables, determine the tension in cable A if cable B suddenly fails. Assume the beam is a slender rod.

The 500-lb beam is supported at A and B when it is subjected to a force of 1000 lb as shown. If the pin support at A suddenly fails, determine the beams initial angular acceleration and the force of the roller support on the beam. For the calculation, assume that the beam is a slender rod so that its thickness can be neglected.

The solid ball of radius r and mass m rolls without slipping down the 60 trough. Determine its angular acceleration.

By pressing down with the finger at B, a thin ring having a mass m is given an initial velocity v0 and a backspin V0 when the finger is released. If the coefficient of kinetic friction between the table and the ring is k, determine the distance the ring travels forward before backspinning stops.