Question

A particle moves in a circle of radius 4m with a linear speed of 20m//s. Find the angular speed.

Answer 1

The angular speed of the particle = 5 rad/s

Given :

A particle moves in a circle of radius 4m with a linear speed of 20m/s

To find :

The angular speed of the particle

Solution :

Step 1 of 2 :

Write down the radius and linear speed

Here it is given that the particle moves in a circle of radius 4 m with a linear speed of 20m/s

Radius = r = 4 m

Linear speed = v = 20 m/s

Step 2 of 2 :

Calculate angular speed of the particle

We know that the relationship between linear speed and angular speed is

v = rω

Where ,

Radius = r

Linear speed = v

Angular speed = ω

Now by the given ,

Radius = r = 4 m

Linear speed = v = 20 m/s

Angular speed = ω rad/s = ?

Thus we get

v = rω

⇒ 20 = 4 × ω

⇒ ω = 20/4

⇒ ω = 5

Hence angular speed of the particle = 5 rad/s

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Answer 2

Answer:

The angular speed of the particle = 5 rad/s

Explanation:

Angular velocity of a particle is " the rate of velocity at which the object or a particle is rotating around a centre or a specific point in a given time period."  Angular velocity is a vector quantity that expresses both magnitude and direction while angular speed expresses only magnitude. They are both represented with same formula.

Given :

Circle of radius  = 4m

linear speed of the particle = 20m/s

To be calculated

The angular speed of the particle

Here it is given that the particle moves in a circle of radius 4 m with a linear speed of 20m/s

So, Radius = r = 4 m

and, Linear speed = v = 20 m/s

The relationship between linear speed and angular speed is

 v = rω

Where ,

r = Radius

v = Linear speed

ω = Angular speed

r = 4 m

v = 20 m/s

ω rad/s = ?

So, we get

v = rω

20 = 4 × ω

ω = 20/4

ω = 5

Angular speed of the particle = 5 rad/s