Question

Angular speed of second hand of a clock is:
A) $\dfrac{1}{{60}}rad/\sec$
B) $\dfrac{\pi }{{60}}rad/\sec$
C) $\dfrac{{2\pi }}{{60}}rad/\sec$
D) $\dfrac{{360}}{{60}}rad/\sec$

Answer 1

Angular velocity is defined as the ratio of change of angular displacement ${\text{\theta }}$ with respect to time t, and for an object rotating about a fixed axis at a constant speed.

Complete step by step solution:
The seconds hand of a clock completes one rotation in 1 minute i.e 60 seconds.
Angular speed = angle swept by radius vector / time taken
Angle sept for one complete rotation is: $2 \pi radian$
$\Rightarrow \dfrac{{2\pi }}{{{\text{60}}}}{\text{ = }}\dfrac{\pi }{{30}}$
$\therefore \dfrac{\pi }{{30}}{\text{ radians per second}}$

Thus, option C is correct.

The second hand therefore makes one revolution every minute - that is, 1 revolution per minute (rpm), which is 1/60 of a revolution per second, which is 6 degrees per second.
The angular velocity does not depend on the size of the watch, but for larger watches the linear velocity of the points at the end of the hand will be higher.

Note: In everyday speech, "speed" and "speed" are often used interchangeably. In physics, however, these words have special and special meanings. "Speed" is the rate at which an object moves in space and is given only by the unit in specific units (usually meters per second or per hour). Speed, on the other hand, is added speed in one direction. The velocity is then called the scalar quantity, while the velocity is the quantity of a vector.