Question

The speed of motor decreases from $1200rpm$ to $600rpm$ in $20s$. Then the total number of rotations it make before coming to rest will be given as,
$\begin{align}
  & A.400 \\
 & B.600 \\
 & C.800 \\
 & D.1000 \\
\end{align}$

Answer 1

Hint: The speed of the motor should be changed from rotation per minute to revolution per second. Find the angular acceleration of the body. Using this, find out the displacement of the body also. The displacement will be equivalent to the difference between the square of the final velocity and the square of initial velocity which is divided by the twice of the angular acceleration of the body. Substitute the values in it.

Complete answer:
The initial velocity has been mentioned in the question as,
$u=1200rpm$
This has to be converted to revolution per sec, that is,
$u=1200rpm=20rev{{s}^{-1}}$
Similarly, the final velocity has been given as,
$v=600rpm$
In terms of revolutions per second, we can write that,
$v=600rpm=10rev{{s}^{-1}}$
Time taken for the complete rotation can be written as,
$t=20s$
The angular acceleration of the body is the ratio of the difference of initial and final velocities to the time taken. This can be expressed in an equation as,
$a=\dfrac{v-u}{t}$
Substituting the values in it will give,
$a=\dfrac{10-20}{20}=0.5rev{{s}^{-1}}$
Now let us find out the displacement of the body. At the end the motor is coming to rest. Therefore the final velocity will be zero.
$v=0$
That time the initial velocity will be given as,
$u=20rev{{s}^{-1}}$
The displacement will be equivalent to the difference between the square of the final velocity and the square of initial velocity which is divided by the twice of the angular acceleration of the body. This can be written as an equation,
$s=\dfrac{{{v}^{2}}-{{u}^{2}}}{2a}$
Substituting all the values in the equation can be shown as,
$s=\dfrac{-{{20}^{2}}}{2\times -0.5}$
Simplifying this equation will give us the final answer required. That is,
$s=400$

So, the correct answer is “Option A”.

Note:
Angular velocity is defined as the time rate of change of the variation is angular velocity. There are two types of angular accelerations in general. One is orbital angular acceleration and the spin angular acceleration. It is considered to be a vector quantity.