An electric motor spins at 1000 rpm and is slowing down at a rate of 10 t rad/s2 ; where t is measured in seconds. (a) If the motor radius is 7.165 cm, what is the tangential component of acceleration at the edge of the motor at t = 1.5 seconds? (b) How long will it take, in seconds, to decrease its angular velocity by 75%?

a) The tangential component of acceleration at the edge of the motor at   is -1.075 meters per square second.

b) The electric motor will take approximately 3.963 seconds to decrease its angular velocity by 75 %.

Explanation:

The angular aceleration of the electric motor (), measured in radians per square second, as a function of time (), measured in seconds, is determined by the following formula:

(1)

The function for the angular velocity of the electric motor (), measured in radians per second, is found by integration:

(2)

Where is the initial angular velocity, measured in radians per second.

a) The tangential component of aceleration (), measured in meters per square second, is defined by the following formula:

(3)

Where is the radius of the electric motor, measured in meters.

If we know that , and , then the tangential component of the acceleration at the edge of the motor is:

The tangential component of acceleration at the edge of the motor at   is -1.075 meters per square second.

b) If we know that and , then the time needed is:

The electric motor will take approximately 3.963 seconds to decrease its angular velocity by 75 %.

d.7.5cm is your answer