Question

If the length of the second's hand in a stop-clock is 3 cm, then the angular velocity and linear velocity of the tip is

• (A) 0.2047 rad/s and 0.0314 ms^-1
• (B) 0.2547 rad/s and 0.314 ms^-1
• (C) 0.1472 rad/s and 0.06314 ms^-1
• (D) 0.1047 rad/s and 0.00314 ms^-1

Answer 1

The Correct Option is D

Explanation:
Angular velocity of second's hand$$\begin{array}{l}=\frac{2\pi }{60}\\ =\frac{\pi }{30}\\ =\frac{3.14}{30}\\ =0.1047\mathrm{rad}/\mathrm{s}\end{array}$$Linear velocity, $v=r\omega$$$\begin{array}{l}=3\times {10}^{-2}\times 0.1047\\ =0.00314\mathrm{m}/\mathrm{s}\end{array}$$

Answer 2

Linear Velocity

Linear velocity is defined as the rate of change of displacement of a body moving along a straight path. It is denoted by v.

• The SI unit of linear velocity is meter per second (m/s). 
• It is a vector quantity. 
• For an object having circular motion, the linear velocity is along the circumference of the circle.
• It varies at every point on the circle.

Angular Velocity

Angular velocity of a rotating body is defined as the rate of change of its angular position. It is denoted by omega (ω).

• The SI unit of angular velocity is radian per second (rad/s).
• It is a vector quantity.
• For an object having circular motion, the angular velocity is along the axis of rotation.

Relation Between Linear Velocity and Angular Velocity

For a body moving in a circle of radius r, then the relation between its linear velocity and angular velocity is given by

v = rω