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