During a testing process, a worker in a factory mounts a bicycle wheel on a stat

Question

During a testing process, a worker in a factory mounts a bicycle wheel on a stationary stand and applies a tangential resistive force of 120 N to the tire's rim. The mass of the wheel is 1.70 kg and, for the purpose of this problem assume that all of this mass is concentrated on the outside radius of the wheel. The diameter of the wheel is 60.0 cm. A chain passes over a sprocket that has a diameter of 9.25 cm. In order for the wheel to have an angular acceleration of 4.10 rad/s2, what force must be applied to the chain? (Enter the magnitude only.)

Explanation / Answer

The rotational inertia of the bicycle wheel is mr2 = (1.70 kg)(0.30 m)2 = 0.153 kg m2

We know ? = I? therefore the net torque must be (0.153 kg m2)(4.10 s-2) = 0.6273 Nm

The torque applied must counteract the resistive torque of (120 N)(0.30 m) = 36 Nm therefore we need a total applied torque of 36.6273 Nm

Since the chain applies force on a radius of 4.625 cm = 0.04625 m, the applied force must be

(36.6273 Nm)/(0.04625 m) = 792 N

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