An electric motor rotating a workshop grinding wheel at a rate of 1.31 ✕ 102 rev/min is switched off. assume the wheel has a constant negative angular acceleration of magnitude 3.40 rad/s2. (a) how long does it take for the grinding wheel to stop? (b) through how many radians has the wheel turned during the interval found in (a)?

(a) 4.03 s

The initial angular velocity of the wheel is

The angular acceleration of the wheel is

negative since it is a deceleration.

The angular acceleration can be also written as

where

is the final angular velocity (the wheel comes to a stop)

t is the time it takes for the wheel to stop

Solving for t, we find

(b) 27.6 rad

The angular displacement of the wheel in angular accelerated motion is given by

where we have

is the initial angular velocity

is the angular acceleration

t = 4.03 s is the total time of the motion

Substituting numbers, we find

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