Question

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

Answer 1

Hint: Find the number of rotations in one second. Determine the angle the wheel goes through in degrees using the fact that one revolution is 360 degrees. Then use the conversion factor $\dfrac{\pi }{{180}}$ to convert degrees into radians.

Complete step-by-step answer:
The angle is the figure formed by the two rays meeting at a common point. The angle can be measured either in units of degree or radians.
In the given question, the common point is the center of the wheel and the rays are the initial and final position of any line on the wheel.
It is given that the wheel makes 360 revolutions in one minute. Then to find the number of revolutions in one second, we divide 360 by 60.
Number of revolutions in one second = $\dfrac{{360}}{{60}}$
Number of revolutions in one second = $6rev/\sec$
Hence, the wheel makes 6 revolutions per second.
We know that one revolution is 360 degrees. Then the 6 revolution is 6 times 360 degrees.
Number of degrees = $6 \times 360^\circ$
Number of degrees = 2160°
We now convert 2160° into radians.
We know that 180° is equal to $\pi$ radians. Then, we have:
$2160^\circ = \dfrac{\pi }{{180^\circ }} \times 2160^\circ$
$2160^\circ = 12\pi rad$
Hence, the correct answer is $12\pi$ radians.

Note: You can also directly convert the number of revolutions into radians by multiplying with $2\pi$ radians to get the answer. This direct method will save time.