Circular Velocity Formula: Definition & Solved Examples

Circular Velocity is the velocity possessed by an object in a uniform circular motion. The motion of an object along the circumference of a circle or rotation along its round direction is called circular motion. The object may be shifting in uniform movement and has a constant angular rate of rotation and speed or a non-uniform motion with changing rate of rotation. Objects moving in circles have a speed that is equal to the distance traveled per time of travel. The average speed of the object can be determined by multiplying the rotational frequency by the circumference.

Circular velocity is directly proportional to the radius of the circular path and is inversely proportional to the time taken by the object. Circular Velocity Formula is defined as the circumference of the circular path divided by the time taken. Circular Velocity Formula is given as v_c = 2πr/T, where, V_c is the circular velocity, r is the radius of the circular path, and T is the time taken.

Key Terms: Circular Velocity, Uniform Circular motion, Radian, Angular Velocity, Motion, Circumference, Circular Path, Radius, Time Taken

---

What is Circular Velocity?

[Click Here for Sample Questions]

Circular Velocity is defined as the velocity of an object along the circumference of a circle or rotation along a uniform circular path. Uniform circular motion is a type of motion in which an object moves in a circular motion at a constant speed whereas the velocity changes at each location due to the changing direction of the velocity vector. 

• The circular velocity is inversely proportional to the time taken by an object. 
• It is directly proportional to the radius of the circular path.
• Circular Velocity is denoted by the symbol v_c.
• Its unit of measurement is m/s.
• The dimensional formula of Circular Velocity is given by [M⁰L¹T^-1].

Circular Velocity 

Read More:

---

Circular Velocity Formula

[Click Here for Sample Questions]

The Circular Velocity Formula is defined as the circumference of the circular path divided by the time taken. Thus, 

The Circular Velocity Formula is expressed as

v_c = 2πr/T

Where 

• R refers to the radius of the circular orbit.
• T refers to the time period.

Circular velocity can also be calculated when angular velocity ω is given. In this case, the Circular Velocity Formula is 

v_c = ωr

Where 

• ω denotes the angular velocity.
• r denotes the radius of the circular path.

Circular Velocity Formula

---

Solved Examples on Circular Velocity Formula

[Click Here for Sample Questions]

Here are a few solved examples of Circular Velocity Formula with detailed solutions to understand the concept better.

Example 1: Find the circular velocity of an object undergoing circular motion when the radius is 5 m for a time of 2 s.

Solution: We have,

• Radius r = 5
• Time T = 2

Using the formula we have,

v_c = 2πr/ T

= (2 × 3.14 × 5)/ 2

= 31.4/ 2

= 15.7 m/s

Thus, the circular velocity of the object is 15.7 m/s.

Example 2: Find the circular velocity of an object undergoing circular motion when the radius is 4 m for a time of 7 s.

Solution: We have,

• r = 4
• T = 7

Using the formula we have,

v_c = 2πr/ T

= (2 × 3.14 × 4)/ 7

= 25.12/ 7

= 3.58 m/s

Therefore, the circular velocity of the given object is 3.58 m/s.

Read More:

---

Things to Remember

• Circular velocity refers to the velocity of an object while undergoing uniform circular motion.
• It is denoted by the symbol v_c and its unit of measurement is m/s. 
• It is directly proportional to the radius of the circular path and is inversely proportional to the time taken.
• Circular velocity is equal to the circumference of the circular path divided by the time taken by the object.
• Circular Velocity Formula is given as v_c = 2πr/T, where r refers to the radius of the circular path and t is the time taken.
• In case angular velocity is given, the Circular Velocity Formula is given as v_c = ωr, where is angular velocity.