9.) This 200 kg
1 answer:
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Answer:
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 %.