A small 460-gram ball on the end of a thin, light rod is rotated in a horizontal
ID: 1292994 • Letter: A
Question
A small 460-gram ball on the end of a thin, light rod is rotated in a horizontal circle of radius 1.5m .
Part A
Calculate the moment of inertia of the ball about the center of the circle.
Express your answer to two significant figures and include the appropriate units.
Part B
Calculate the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.018N on the ball. Ignore air resistance on the rod and its moment of inertia.
Express your answer to two significant figures and include the appropriate units.
Explanation / Answer
A mass on a stick has the same moment of inertia as a thin hoop:
I = mr2
I = (0.46 kg)(1.5)2 = 1.035 kgm2
If the mass is moving at a constant angular velocity, then it is not accelerating, and the only necessary torque merely cancels out the torque applied by the frictional force of .018 N acting at a radius of 1.5 m on the ball:
Since force is applied at a 90o angle to the radius, so the factor sinq becomes 1, and really the torque is:
t = (.018 N)(1.5 m) = .027 Nm