Solved Examples on Tangential Velocity
Example 1: The angular velocity of a circular ring is 20 rad/s, and its diameter is 20 cm. Find its tangential velocity.
Solution:
Given,
Angular velocity, ω = 20 rad/s,
Diameter of the ring, d = 20 cm.
Radius, r = d / 2
= 20 cm/2
= 10 cm
= 0.1 mFormula for Tangential velocity is as given:
vt = r × ω
= 0.1 m × 20 rad/s
= 2 m/s
Example 2: Determine the tangential velocity of a disc that has an angular velocity of 10 rad/s and a radius of 5 m.
Solution:
Given,
Angular velocity, ω = 10 rad/s,
Radius of the disc, d = 5 m.
Formula for Tangential velocity is as given:
vt = r × ω
= 5 m × 10 rad/s
= 50 m/s
Example 3: What is the radius of the wheel which turns with a speed of 10 m/s, and its angular velocity is 5 rad/s?
Solution:
Given,
Tangential velocity, vt = 10 m/s,
Angular velocity, ω = 5 rad/s.
Formula for Tangential velocity is as given:
vt = r × ω
10 m/s = r × 5 rad/s
r = 2 m
Example 4: What is the radius of the ring which has a tangential velocity of 50 m/s, and its angular velocity is 5 rad/s?
Solution:
Given,
Tangential velocity, vt = 50 m/s,
Angular velocity, ω = 5 rad/s.
Formula for Tangential velocity is as given:
vt = r × ω
50 m/s = r × 5 rad/s
r = 10 m
Example 5: If the tangential velocity of a wheel is 22 m/sec, and its angular velocity is 11 radians/sec. Then find out its radius.
Solution:
Tangential velocity, vt = 22 m/sec
Angular velocity, ω = 11 radians/sec
Now the formula for tangential velocity is:
Vt = r×ω
r = vt / ω
= 22 / 11
= 2 mThus, radius of the wheel is 2 meters
Tangential Velocity Formula
Linear component of any object’s velocity which is moving on a circular path is called tangential velocity. When an object moves in a circular path at a distance of r from the centre, the velocity of the body is always tangential. It can also be stated that the linear velocity is equal to the tangential velocity at any given time. Let us learn about tangential velocity, formula, examples, and others in this article.
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