You are driving in a 1600 kg proto-type of a car that converts translational kin

Question

You are driving in a 1600 kg proto-type of a car that converts translational kinetic energy into rotational kinetic energy while braking. Assume that you are driving at a speed of 20 m/s on a flat road, and approach a stop sign. If the car can transfer all of its translational kinetic energy into rotating a 0.20-m-radius, 20-kg solid- cylinder while stopping, what final rotational speed would the cylinder have? (Assume that the cylinder was not rotating initially and that friction does not exist.) v 20 m/s a, = 0 rad/s vr =0m/s = ? rad/s

Explanation / Answer

M = mass of car = 1600 kg

v = speed of car = 20 m/s

I = moment of inertia of the cylinder = (0.5) m r2 = (0.5) (20) (0.2)2 = 0.4 kgm2

w = rotational speed

using conservation of energy

(0.5) I w2 = (0.5) M v2

(0.4) w2 = (1600) (20)2

w = 1265 rad/s

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