A wheel makes ${360^\circ }$ revolutions in one minute. Through how many radians does it turn in one second?

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Number of revolutions made by the wheel in $1$ minute $=360$

$\therefore$ Number of revolutions made by the wheel in $1$ second $=\frac{360}{60}=6$

In one complete revolution, the wheel turns an angle of $2 \pi$ 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 an angle of $12 \pi$ radian.

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