# Circular Velocity Formula

Last Updated : 04 Feb, 2024

When the velocity changes, the acceleration changes as well, but not in the same direction. As a result, an object moving along a circular path must always have an acceleration that is perpendicular to the velocity. The circular motion can be both uniform and non-uniform. The uniform circular motion formula will be discussed with examples in this topic. Let’s get this topic mastered!

### What is Circular Velocity?

Circular velocity is defined as the velocity possessed by an object while undergoing uniform circular motion. Uniform circular motion is a two-dimensional motion in which an object moves in a circular motion at a constant speed while the velocity changes at each location due to the changing direction of the velocity vector.Â

Â

The circular velocity is directly proportional to the radius of the circular path but inversely proportional to the time taken by the object.Â

• It is denoted by the symbol vc.Â
• Its unit of measurement is m/s.Â
• And the dimensional formula is given by [M0L1T-1].Â

### Circular Velocity Formula

Mathematically, it is defined as the circumference of the circular path divided by the time taken.

vc = 2Ï€r/T

where,

• vc is the circular velocity,
• r is the radius of circular path,
• T is the time taken.

However, the circular velocity can also be calculated when angular velocity Ï‰ is given and it is calculated as,

vc = Ï‰ r

where,Â

• Ï‰ is the angular velocity,
• r is the radius of the circular path

### Sample Problems

Problem 1: Calculate the circular velocity of an object undergoing circular motion if the radius is 3 m for a time of 4 s.

Solution:

We have,

r = 3

T = 4

Using the formula we have,

vc = 2Ï€r/T

= (2 Ã— 3.14 Ã— 3)/4

= 18.84/4

= 4.71 m/s

Problem 2: Calculate the circular velocity of an object undergoing circular motion if the radius is 5 m for a time of 2 s.

Solution:

We have,

r = 5

T = 2

Using the formula we have,

vc = 2Ï€r/T

= (2 Ã— 3.14 Ã— 5)/2

= 31.4/2

= 15.7 m/s

Problem 3: Calculate the circular velocity of an object undergoing circular motion if radius is 4 m for a time of 7 s.

Solution:

We have,

r = 4

T = 7

Using the formula we have,

vc = 2Ï€r/T

= (2 Ã— 3.14 Ã— 4)/7

= 25.12/7

= 3.58 m/s

Problem 4: Calculate the radius if the circular velocity of an object undergoing circular motion is 5 m/s for a time of 3 s.

Solution:

We have,

vc = 5

T = 3

Using the formula we have,

vc = 2Ï€r/T

=> r = vcT/2Ï€

= (5 Ã— 3)/(2 Ã— 3.14)

= 15/6.28

= 2.38 m

Problem 5: Calculate the radius if the circular velocity of an object undergoing circular motion is 8 m/s for a time of 2 s.

Solution:

We have,

vc = 8

T = 2

Using the formula we have,

vc = 2Ï€r/T

=> r = vcT/2Ï€

= (8 Ã— 2)/(2 Ã— 3.14)

= 16/6.28

= 2.54 m

Problem 6: Calculate the time if the circular velocity of an object undergoing circular motion is 7 m/s for a radius of 5 m.

Solution:

We have,

vc = 7

r = 5

Using the formula we have,

vc = 2Ï€r/T

=> T = 2Ï€r/vcÂ

= (2 Ã— 3.14 Ã— 5)/7

= 31.4/7

= 4.48 s

Problem 7: Calculate the time if the circular velocity of an object undergoing circular motion is 12 m/s for a radius of 8 m.

Solution:

We have,

vc = 12

r = 8

Using the formula we have,

vc = 2Ï€r/T

=> T = 2Ï€r/vc

= (2 Ã— 3.14 Ã— 8)/12

= 50.24/12

= 4.18 s

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