Question

Calculate the angular velocity and linear velocity of tip of minutes hand of length 10 cm

Answer 1

Radius of tip of minute hand = r = 10 cm = 0.1 m

As minute hand takes one hour to complete one rotation (i.e. 360^o 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

$V=r\times w$

V = 0.1 X 1.745 X 10 ^-3

V = 1.745 X 10 ^-4 m/s