A human-sized version of the popular \"hamster wheel\" is shaped like a cylindri
ID: 2258024 • Letter: A
Question
A human-sized version of the popular "hamster wheel" is shaped like a cylindrical shell and has a radius of 2.25 m. Its total mass is 110 kg, assumed to be concentrated around the outer edge.
(a) What is the moment of inertia of the wheel?
(b) A person running on the wheel applies a horizontal force of 148 N to the bottom of the wheel. What torque does he supply?
(c) What is the magnitude of the angular acceleration of the wheel while the person runs on it? Assume that his torque is the only torque acting on the wheel (i.e. ignore friction).
(d) Assume the wheel starts from rest, and the person accelerates it for 1.7 s. Through what angle (in rad) does the wheel move during this time?
Explanation / Answer
M.O.I =M*R^2
= 110*2.25^2 =
556.88 kg.m2
Torque = F*r
= 148*2.25
= 333 N.m
T = I*angular acc
333 = 556.88 *ang. acc.
ang.acc = 0.598 rad/s2
ang. displacement = 1/2*0.598 *1.7^2
= 0.864 rad
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