(a) How long does it take the grinding wheel to stop? s (b) Through how many rad

Question

(a) How long does it take the grinding wheel to stop?
s

(b) Through how many radians has the wheel turned during the time interval found in part (a)?
rad

An electric motor rotating a workshop grinding wheel at 1.20 An electric motor rotating a workshop grinding whe 102 rev/min is switched off. Assume the wheel has a constant negative angular acceleration of magnitude1.94 rad/s^2. (a) How long does it take the grinding wheel to stop? s (b) Through how many radians has the wheel turned during the time interval found in part (a)? rad

Explanation / Answer

Given,

angular acceleration of the wheel = -1.94 rad/sec^2

initial angular velocity = 1.2 * 10^2 rev/min

initial angular velocity = 12.566 rad/sec

final angular velocity = 0 rad/sec

by equation of motion

final velocity = initial velocity + acceleration * time

0 = 12.566 - 1.94 * time

time = 6.477 sec

it will take 6.477 sec to stop the grinding wheel

by equation of motion

final velocity^2 = initial velocity^2 + 2 * acceleration * distance

0 = 12.566^2 - 2 * 1.94 * distance

distance = 40.69 rad

wheel has turned 40.69 rad

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