Question

If motor revolving at $1200$ rpm slows down uniformly $900$ rpm in $2$ seconds. Calculate the angle axis rotation of the motor and the number of revolution it makes during this time.

Answer 1

The angular velocities are given as,

${\omega }_1=1200rpm$

${\omega }_1=40\pi rad/s$

${\omega }_2=900rpm$

${\omega }_2=30\pi rad/s$

The angular acceleration is given as,

$\alpha =\frac{40\pi -30\pi }{2}$

$\alpha =5\pi rad/s^2$

The angle is given as,

$\theta ={\omega }_{1}t+\frac{1}{2}\alpha t^2$

$\theta =40\pi \times 2+\frac{1}{2}\times 5\pi {\left(2\right)}^2$

$\theta =90\pi rad$

The numbers of revolutions are given as,

$n=\frac{90\pi }{2\pi }$

$n=45rev$