Question

Calculate the angular velocity and linear velocity of a tip of minute hand of length 10 cm.
(Ans : 1.745 x 10⁻³ rad/s, 1.745 x 10⁻⁴ m/s)

Answer 1

Given –

Radius of tip of minute hand = r  = 0 cm    = 0.1 m

As minute hand takes one hour to complete one rotation (i.e. 360o or 2 π radian)

The time period of the tip of minute hand can be given as

=  T            =      1hr           =  60 min      = 3600 sec

The angular velocity of any particle performing circular motion can be given as time rate of change of angular displacement

W = (dθ)/ (dt)

W= (2 π) / T

W= (2 X 3.14 ) / 3600

W= 1.745 X 10 -3 rad / sec

The linear velocity (v) at the tip of minute hand is

V = r X w

V = 0.1  X 1.745 X 10 -3

V = 1.745 X 10 -4 m/