Question

A wheel makes $360$ revolutions in one minute, through how many radians does it turn in one second ?

Answer 1

Given that a wheel makes 360 revolutions in 1 minute.

ie a wheel makes 360 revolutions in 60 seconds.

$\therefore$ In 1 second, no. of revolutions = $\frac{360}{60}$

= 6 revolutions

In 1 revolution, the angle made by the wheel = ${360}^{\circ }$

$\therefore$ Angle made by the wheel in 6 revolutions = $6\times {360}^{\circ }$

$={2160}^{\circ }$

Radian made in 6 revolutions = ${2160}^{\circ }\times \frac{\pi }{{180}^{\circ }}$

$=12\pi$