Three Rotating Objects with Identical Torque (2)
Three objects (from left to right, solid disk, solid sphere, and hoop) of identical mass m and radius R are mounted at rest on frictionless axles. Each object has a string of the same length wrapped around it. Each string is then pulled with an identical force F for the same time interval; the strings do not slip. The mass of the spokes on the hoop is negligible.
Which of the objects will have the most angular momentum at the end of the interval?
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1 solution
Each of the three objects is subject to the same net torque because the force in each case is the same, and the radius of each object is the same. Since the time intervals are the same, and the angular impulse is defined by torque times time, the change in each object's angular momentum will be the same. Therefore, the objects will have the same angular momentum at the end of the interval.