Chapter 4 readings
Chapter 4 readings PHSX 205-001
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This 4 page Class Notes was uploaded by Rebeka Jones on Monday September 19, 2016. The Class Notes belongs to PHSX 205-001 at Montana State University taught by Dr. Greg Francis in Fall 2016. Since its upload, it has received 5 views.
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Date Created: 09/19/16
Chapter 4: Two-Dimensional Kinematics It takes 1 number to specify a position on a 1-dimensional line, 2 numbers for a 2-dimensional space, and 3 numbers for a 3-dimensional space. To create a coordinate system in 2-dimensions take a point at the origin and define two perpendicular directions to orient the system. *curly notaion with magnitude and direction as the two number s; it is polar plane system Paraenthesis notation with two numbers as compoents; Cartesian coordinates. Anything moving along a curved path has an instantaneous velocity vector whose direction is tangent to the curve, at each point of the path, and whose magnitufe is the instantaneous speed of the object along the path. Acceleration is the rate of change of velocity, not speed. -acceleration includes change in direction just because something accelerated does not mean it speeds up. Acceleration is in the same direction as the velocity. -object speeds up going in the same direction Acceleration has a forward component and a perpendicular component -velocity vector gets longer and turns in direction of perpendicular compoment Acceleartion is perpendicular to the velocity -object turns but speed is not changed Acceleration has a backward component and perpendicular component -velocity vector gets short and turns Acceleration is in the opposite diection as the velocity -object slows down going in the same direction *small perpendicular acceleration produces small change in direction, but change in the velocity magnitude is tiny, essentiall negliagable. Projectile motion – the motion of objects thrown through the air *can be described in 2-dimensions. Only if there are factors such as wind does it require a 3 dimension. 2 Objects in free fall experience downward acceleration of 10 m/s (gravity) Relationship between of the angles between the acceleration and velocity vectors Speeding up -less than 90° Slowing down -more than 90° 2 Constant speed -at 90° You must divide projectile motion problems into horizontal (constant speed) and vertical (10 m/s/s down) and treat the components seperatly. Important -Be explicit about your choices of coordinate system and varables and be careful not to make any unjustified assumptions. -Treat the two components of motion sperately, but recognize the places where the answer from the analysis of one direction may determine something about the other motion. Remember that even though something is moving at a constant speed, it accelerates if its direction changes. If an object is moving along a curved path at constant speed the acceleration much always be perpendicular to the celocity. If the path is circular, th e acceleration vector must lie along a radial line, since radial lines at lines that are perpendicular to the circumference of the circle points. Because acceleration always points toward the center, the acceleration of an object undergoing uniform circular motion is called the centripetal acceleration. ▯ ???? ???? = ???? *all velocities are relative to the point of origin 3 Chapter Formulas A 2-dimensional problem may be divided into two 1-dimensional problems. Then for constant acceleration a ix the x-direction and a inythe y-direction) we have ???? = ???? + ???? ∆???? Same for y just ▯▯ ▯▯ ▯ 1 substitute x with ∆???? = ????▯▯ ???? ▯▯ ∆???? 2 y 1 ▯ ∆???? = ???? ∆▯▯+ 2 ????▯∆???? ▯ ▯ ????▯▯ = ???? ▯▯ + 2???? ▯???? ▯▯ For uniform circular motion, the acceleration toward the center is ???? = ▯ The velocity addition formula for origins, B and C is ???? ▯,▯ = ???? ▯,▯+ ???? ▯,▯ 4
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