Purpose: To investigate the conservation of angular momentum about a point that is external to a rolling ball.
Process: First, we measure the ball's mass and diameter. m=0.0289 kg, D=0.019 m.
In order to determine the horizontal velocity of the ball as it rolls off the end of the ramp, we place the ramp on the edge of a table. We release the ball at a marked point, and we use the carbon paper to mark the landing point of the ball. Then, we measure the distances L and high h. L=0.595 m, h=0.955 m.
We use:
(gt^2)/2=h
Vx*t=L
Vx=1.348 m/s
We set up the rotating disk by using the aluminum top disk, and mount the ball-catcher on top of the small torque pulley using a gray-capped thumbscrew. We hang a mass, m=0.0246 kg, on the pulley, rp=0.02495 m, rotate the disk to raise the mass to the top, and release it. We start the sensor and collect the angular acceleration. |αup|=5.92 rad/s^2, |αdown|=5.27 rad/s^2, |αave|=5.6205 rad/s^2.
We already know the equation for the moment of inertia, and we use it to get the moment:
I=(mgrp)/α-mr^2
I=0.001055 kg*m^2
We poition the ramp perpendicular to the ball-catcher, and the end of the ramp should have same high as the catcher so that the ball can be caught by the catcher. We release the ball in the same mark which is same as the mark in first process.
We place the ramp in two different position so that the ball can be caught by the catcher in different position. We measure the distance from the ball to the center of the rotation, r, and collect the angular velocity of the disk, ω.
① ω=2.269 rad/s r=0.076 m
② ω=1.353 rad/s r=0.042 m
Finally, we want to compare the theoretical angular velocity and the experimental angular velocity. Therefore, we use:
r*m*Vx=Iω+[(3/5)mrb^2+mr^2]
① ω=2.269 rad/s r=0.076 m
Theoretial ω=2.42 rad/s
Experimental ω=2.269 rad/s
6% off
② ω=1.353 rad/s r=0.042 m
Theoretial ω=1.478 rad/s
Experimental ω=1.353 rad/s
8% off
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