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

Vedclass pdf generator app on play store
Vedclass iOS app on app store

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.

Similar Questions

If $a\,{\cos ^3}\alpha + 3a\,\cos \alpha \,{\sin ^2}\alpha = m$ and $a\,{\sin ^3}\alpha + 3a\,{\cos ^2}\alpha \sin \alpha = n,$ then  ${(m + n)^{2/3}} + {(m - n)^{2/3}}$ is equal to

Find the value of $\sin 15^{\circ}$

Observe that, at any instant, the minute and hour hands of a clock make two angles between them whose sum is $360^{\circ}$. At $6: 15$ the difference between these two angles is  $....^{\circ}$

  • [KVPY 2012]

In a circle of diameter $40 \,cm ,$ the length of a chord is $20 \,cm .$ Find the length of minor arc of the chord.

Find the degree measures corresponding to the following radian measures (Use $\pi=\frac{22}{7}$ ).

$\frac{11}{16}$