Question

A gramophone disc is rotating at 78 rotations per minute.Due to power cut, it comes to rest after 30 s. The angular retardation of the disc will be:
A 0.27 $radians/ sec^2$
B 0.127 $radians/ sec^2$
C 12.7 $radians / sec^2$
D 0 $radians / sec^2$

Answer 1

Hint: Angular acceleration and angular velocity analogous to linear acceleration and linear velocity respectively.

Complete step by step answer:
Angular acceleration ($\alpha $ )=($\omega_f$ -$\omega_i$)/t
Where, $\omega_f$ is the final angular velocity of the gramophonic disc,
                $\omega_i$ is the initial angular velocity of the gramophonic disc,
                  And, t is the time.
$\omega $=2$\pi $/t OR 2 $\pi $f
Where f is the frequency.
It is given to us that the disc makes 78 rotations in 1 minute.
So the frequency (f)=$\dfrac{78}{60}$
[frequency is the no. Of rotations made by the disc in 1 second.]
Time is 30 seconds.
So, Angular acceleration ($\alpha $) =0-2 $\pi $f/t
                                               = - 2 $ \times $$\pi $ $ \times $78/60 $ \times $ 30
$ \Rightarrow $ -0.272 $radians/s^2$

Note:The negative symbol in the angular acceleration represents that the disc is retarding which means acceleration is in opposite to the direction of motion of the disc.