Question

A phonograph turn table rotates at 50 rev/min. Its angular speed in rad/sec is

• A. $8.164\mathrm{rad}.{\sec }^{-1}$
• B. $5.23\mathrm{rad}.{\sec }^{-1}$
• C. $52.3\mathrm{rad}.{\sec }^{-1}$
• D. $81.64\mathrm{rad}.{\sec }^{-1}$

Answer 1

The correct option is B

$5.23\mathrm{rad}.{\sec }^{-1}$

Angular speed

Angular speed is defined as the rate of change of angular displacement, and it is expressed as follows:

$\mathrm{\omega }=\frac{\mathrm{\theta }}{\mathrm{t}}$

Here, $\mathrm{\theta }$ is the angular displacement, $\mathrm{t}$ is time and $\mathrm{\omega }$ is the angular speed.

Find the angular speed of phonograph

It is given that, a phonograph turn table rotates at $50\mathrm{rev}/\min$.

We have to find the angular speed of the phonograph in $\mathrm{rad}/\mathrm{s}$.

As we know that, $1$revolution means $2\pi or6.28$ radian and $1$ minute is equal to $60$ seconds.

Therefore,

$50\mathrm{rev}/\min =\frac{50\times 6.28}{60}$

$=5.24rad/s$

So, the angular speed of the phonograph turn table is approximate $5.23\mathrm{rad}/\sec$.

Hence, option $\mathrm{B}$ is correct answer .