Question

A particle is moving along a circle of radius 10 m at a constant speed of 5 m/s.Find (I) centripetal acceleration and (II) angular speed of the particle.

Answer 1

Given that:

• Radius = 10m
• Speed = 5 m/s

Need to find:

• (I) Centripetal acceleration
• (II) Angular speed of the particle

Solution:

Given,

• v = 5 m/s
• r = 10 m

Formula to find the centripetal acceleration —

${\qquad}{\bigstar{\boxed{\bold{{a}_{r} = \frac{ {v}^{2} }{r}}}}}$

According to the question—

$\sf \implies \: {a}_{r} = \frac{ {(5 \frac{m}{s} )}^{2} }{10m} \\ \\ \sf \implies \: {a}_{r} = \frac{25}{10} \frac{m}{ {s}^{2} } \\ \\ \sf \implies \: {a}_{r} = 2.5 \frac{m}{ {s}^{2} }$

Hence,centripetal acceleration is 2.5 m/s^2.

Formula to find the angular velocity —

${\qquad}{\bigstar{\boxed{\bold{\sf{\omega = \frac{v}{r}}}}}}$

According to the question —

$\sf \implies \omega \: = \frac{5}{10} \\ \\ \sf \implies \omega = 0.5 \frac{radian}{s}$

Hence,the angular speed of the particle is 0.5 radian/s.