A car wheel with a moment of inertia of 7.85 kg.m^2 is accelerating from 2160 rp

Question

A car wheel with a moment of inertia of 7.85 kg.m^2 is accelerating from 2160 rpm to 5040 rpm in a time of 10.0s.  Calculate the following:

a) The torque ( assumed constant) applied to the wheel.

b) The work done in raising the rotation frequency

c) The power (in watts and in horsepower) of the system rotating the wheel.

Hint: does the moment of inertia of a car change as it rotates?

Explanation / Answer

a). w1 = 2160 rpm = 226.08 rad/s w2 = 5040 rpm = 527.52 rad/s T = I*alpha = 7.85* [(527.52 -226.08)]/10 = 236.63 N-m b). W = change in rotational K.E. = 0.5*I *(w2^2 - w1^2) => W = 0.5*7.85*(527.52^2 - 226.08^2) = 891623.35 J c). P = W/t = 891623.35/10 = 89162.335 W = 89162.335/746 hp = 119.52 hp

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