Question

A body moves in a circle with increasing angular velocity at time t=6sec, the angular velocity is 27 radian'sec what is the radius of the circle when linear velocity is 81cm/s.

Answer 1

Answer:

v = r x w

81= r 27

r = 81/27= 3 cm

Answer 2

Therefore the radius of the circle is 0.03 m or 3 cm.

Given:

The angular velocity of the body = ω = 27 rad/s

Linear velocity of the particle = v = 81 cm/s

Time = 6 seconds

To Find:

The radius of the circle.

Solution:

The given question can be solved as shown below.

Let the radius of the circle be 'r'.

Given that,

The angular velocity of the body = ω = 27 rad/s

Linear velocity of the particle = v = 81 cm/s = 81 × 10⁻² m/s = 0.81 m/s

The relation between linear velocity and angular velocity can be stated as shown below,

⇒ Linear velocity (v) = Radius of the circle (r) × Angular velocity (ω)

⇒ v = r × ω

⇒ 0.81 = r × 27

⇒ r = 0.81/27 = 0.03 m = 3 cm

Therefore the radius of the circle is 0.03 m or 3 cm.

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