Question

A turntable rotates at $100 rev/min$. calculate the angular speed in rad/s and in degree/s.

Answer 1

In this problem,we are going to apply the concept of rotational motion. We know that one revolution completes $2\pi \,{\text{radians}}$ and also 360 degrees and one minute has 60 seconds.

Complete step by step answer:
We know that the complete circle has $2\pi \,{\text{radians}}$and one minute has 60 seconds.
Since one revolution completes $2\pi \,{\text{radians}}$, 100 revolutions complete $2\pi \times 100\,{\text{radians}}$.
Therefore, 100 rev/min converts into rad/s as follows,
$100\,{\text{rev}}/\min = \dfrac{{100\left( {\left( {1\,rev} \right)\left( {\dfrac{{2\pi \,rad}}{{1\,rev}}} \right)} \right)}}{{\left( {1\,\min } \right)\left( {\dfrac{{60\,s}}{{1\,\min }}} \right)}}$
$\omega \Rightarrow \dfrac{{10}}{3}\pi \,rad/s$
Also, we know that one revolution is equal to 360 degrees.
Therefore, 100 rev/min converts into degree/s as follows,
$100\,{\text{rev}}/\min = \dfrac{{100\left( {\left( {1\,rev} \right)\left( {\dfrac{{360^\circ }}{{1\,rev}}} \right)} \right)}}{{\left( {1\,\min } \right)\left( {\dfrac{{60\,s}}{{1\,\min }}} \right)}}$
$\omega \Rightarrow 600\,{\text{degree}}/{\text{s}}$
Therefore, 100 rev/min is equal to 600 degree/s.

Note: Once you convert rev/min into rad/s, you can directly convert rad/s into degree/s by multiplying the answer by $\dfrac{{180^\circ }}{\pi }$. Here, the conversion of 100 rev/min into rad/s is $\dfrac{{10}}{3}\pi$. Therefore, the direct conversion of this quantity into degree/s is $\dfrac{{10}}{3}\pi \,rad/s \times \dfrac{{180^\circ }}{\pi } = 600\,{\text{degree/s}}$.