Question

Calculate the angular velocity and linear velocity of a tip of minute hand of length $10$ cm.

Answer 1

Given –Radius of tip of minute hand = r = 0 cm

= 0.1 mAs 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 displacementW = $\frac{\left(d\theta \right)}{\left(dt\right)}$

$W=\frac{\left(2\pi \right)}{TW}=\frac{(2\times 3.14)}{3600W}=1.745\times 10-3rad/sec$

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

$V=r\times \omega$

$V=0.1\times 1.745\times 10-3V=1.7451\times 0-4m/s$