# After the motor is turned off, how many revolutions does the rotor turn before it comes to rest?The rotor of a motor is rotating at 400 rpm when it is turned off. Due to friction, the angular...

After the motor is turned off, how many revolutions does the rotor turn before it comes to rest?

The rotor of a motor is rotating at 400 rpm when it is turned off. Due to friction, the angular acceleration of the rotor after the motor is turned off is -0.1*`omega` rad/s^2, where `omega` is the angular velocity in rad/s.

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This question has been moved to the Math section to incorporate the math symbols required while solving it.

The rotor of a motor is rotating at 400 rpm when it is turned off. Due to friction, the angular acceleration of the rotor after the motor is turned off is -0.1*`omega` rad/s^2, where `omega` is the angular velocity in rad/s.

400 rpm = `(400*2*pi)/60` = 41.88 rad/s

Angular acceleration `alpha = (d omega)/(dt)`

`(d omega)/(dt)` can be written as `((d omega)/(d theta))*((d theta)/(dt))` = `((d omega)/(d theta))*omega`

`alpha = ((d omega)/(d theta))*omega = -0.1*omega`

when the rotor stops `omega = 0`

`int_(41.88)^0 dw = int_(0)^theta -0.1* d theta`

=> `-41.88 = -0.1*theta`

=> `theta` = 418.8 rad

=> `theta` = `418/(2*pi)` revolutions

=> ` theta` = 66.6 revolutions

**The rotor turns 66.6 revolutions before it finally comes to a stop.**

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