There is an animation on a coordinate plane with a circle and its radius. It inc

Question

There is an animation on a coordinate plane with a circle and its radius. It includes the circle rolling on a flat surface. When I play the animation it shows the time and I can stop the animation when needed and measure the position of any point on the coordinate plane.

A 5 kg wheel (a uniform disk) rolling on a rough surface eventually stops as shown in the animation (position of the center of mass and position of a point on the edge of the wheel are shown in meters and time is shown in seconds). What is the magnitude of the average torque about the central axis exerted by friction on the wheel?

Explanation / Answer

Torque, net, average = I*alpha, I being moment of inertia, alpha = average angular acceleration. For a uniform disk, I=0.5mr^2=5kg*(radius^2) alpha=(vf-vi)/(tf-ti). vi=v(t=0), vf=v(t=tf). Given your initial velocity from the animation and vf=0 and the time at which it comes to rest, you have alpha. If they give the radius of the disk, then you can find the moment of inertia. Then torque=(-vi)/(tf)*(1/2)*(m)*(r^2)

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