Motion Graphs

Compare two constant acceleration situations:

  1. Straight-line 1-D motion of a ball in freefall
  2. Rotational motion of a disk

We'll set up equivalent situations for the two objects and compare the motion graphs. Let's take up to be positive for the ball, and clockwise to be positive for the disk. The ball experiences an acceleration of 9.8 m/s2 down because of gravity, while the disk experiences an angular acceleration of 9.8 rad/s2 counterclockwise because of a constant force being applied to a string wrapped around the disk.

Motion 1 - Both objects, starting at the origin, are given an initial velocity in the positive direction, and followed until they come instantaneously to a stop. vo = 9.8 m/s and wo = 9.8 rad/s.

Motion 2 - Both objects start from rest from a positive initial position (4.9 m for the ball, 4.9 rad for the disk). Motion is followed until they reach the origin.

Motion 3 - Both start at the origin and are given an initial positive velocity, and followed until they return to the origin.

Predict what the graphs of position, velocity, and acceleration look like for the two objects in each case.

Note that, aside from the units on the y-axes, the graphs are indistinguishable. The rotational motion is analogous to the straight-line motion in each case.