Question

Q.1 a particle is moving along a circle of radius 50 cm, with a linear velocity of 4 m/s. The angular velocity of the particle is

Answer 1

Question :-

A particle moves in a circle of radius 50m with linear speed 4 m/s.The angular velocity of the particle is -

Answer :-

$\: \: \: \: \: \: \: \: \boxed{ \green{\implies} \sf \: \: \blue{ \omega \:} = \pink{ 0.08\: } \:per \: second } \:$

Explanation :-

Given that :

Radius (r) = 50 m

linear speed (v) = 4 m/s

Angular velocity = ?

We know that :-

$\implies \sf \: v \: = \: r \: \omega \: \\ \\ \to \sf \red{ v \: is \: linear }\: speed \: , \: r \: is \: radius \: and \\ \: \: \: \: \: \: \omega \sf \: \green{is \: angular \:} velocity \:$

Now replace the given values -

$\red{\implies \: } \: 4\: \: \green{ = 50 \: \times \omega \: } \\ \: \\ \implies \: \sf \: \omega \: = \frac{4}{50} \\ \\ \: \: \: \: \: \: \: \: \boxed{ \green{\implies} \sf \: \: \blue{ \omega \:} = \pink{ 0.08 \: } \:per\: second }$