Question

Consider a particle moving around a circle with a radius of 38cm. It rotates from 10 degrees to 100 degrees in 11 seconds. Calculate the instantaneous velocity of the particle.

Answer 1

Step-by-step explanation:

Given that,

Radius of circle, r = 38 cm = 0.38 m

It rotates form 10 degrees to 100 degrees in 11 seconds i.e.

$\theta_i=10^{\circ}=0.174\ rad$

$\theta_f=100^{\circ}=1.74\ rad$

Let $\omega$ is the angular velocity of the particle such that, $\omega=\dfrac{\omega_f-\omega_i}{t}$

$\omega=\dfrac{1.74-0.174}{11}$

$\omega=0.142\ rad/s$

We need to find the instantaneous velocity of the particle. The relation between the angular velocity and the linear velocity is given by :

$v=r\times \omega$

$v=0.38\times 0.142$

v = 0.053 m/s

So, the instantaneous velocity of the particle is 0.053 m/s. Hence, this is the required solution.