Question

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

Answer 1

Hint: here we go through the first unitary method to find the no of revolution in one second and then multiply that no of revolution to the radian that does in one revolution.

Complete step-by-step answer:
Here in the question it is given that a wheel makes 360 revolutions in one minute.
And we know that one minute contains 60 seconds. So we can say that,
In 60 seconds the wheel makes 360 revolutions.
And by applying unitary method we can say,
Number of revolutions made by the wheel in 1 second$={\displaystyle \frac{360}{60}}=6$ revolutions.
As we know in one complete revolution, the wheel turns at an angle of 2π radian.
Hence, in 6 complete revolutions, it will turn an angle of $6\times 2\pi$ radian, i.e. $12\pi$ radian.
Thus, in one second, the wheel turns at an angle of $12\pi$ radian.

Note: Whenever we face such a type of question the key concept for solving the question is to first change the units as in the question the revolution is given in a minute and we have to find the result in second. After that, proceed with the question to get the answer.