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Angular Velocity And Acceleration

1) Automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate (a) its angular acceleration, assumed constant, and (b) the total number of revolutions the engine makes in this time.

2) Pilots can be tested for the stresses of flying high speed jets in a whirling "human centrifuge," Which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed. (a) What was its angular acceleration (assumed constant) and (b) what was its final angular speed in rpm.

3) A small 650 gram ball on the end of a thin, light rod is rotated in a horizontal circle of radius 1.2m. Calculate (a) moment of inertia of the ball about the center of the circle, and (b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020N on the ball. Ignore the rod's moment of inertia and air resistance.

Solution Preview

Initial angular velocity, wo at 4500 rpm = 2*pi*(4500/60) rad/s
Final angular velocity, w at 1200 rpm = 2*pi*(1200/60) rad/s
Time taken to reach to final velocity from initial velocity, t = 2.5 s

w = wo + alpha*t , where alpha = angular acceleration
=> alpha = (w - wo)/t = 2*pi*(1200-4500)/(60*2.5) = -138.226 ...

Solution Summary

Solution also gives the formulas used to solve the problems.