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Tangential Velocity Formula

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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.

What is Tangential Velocity?

Tangential velocity explains the motion of an object along the circle’s edge whose direction is always at the tangent to any given point on the circle.

Hence, Tangential velocity is the component of motion along the edge of a circle measured at any arbitrary instant.

A tangent is a line that only touches one point of a non-linear curve (such as a circle). A two-dimensional graph represents an equation with the relationship between the coordinates x and y. 

In a circular motion, the tangential velocity is the measurement of the speed at any point tangent to the revolving wheel. Through the formula, angular velocity ω is connected to tangential velocity, Vt. Tangential velocity is the component of motion along the circle’s edge that may be measured at any time. 

Also Check, Velocity

Tangential Velocity Formula

First, we must determine the angular displacement θ, which is defined as the ratio of the length of the arcs traced by an item on this circle to its radius ‘r’.

The angular velocity of an object is the rate at which its angular displacement changes. Its standard unit is radians per second, and it is represented by ω. It differs from linear velocity in that it only considers objects that move in a circular motion. As a result, it is used to calculate the rate at which angular displacement is swept.

Tangential Velocity Formula

 

Mathematically, the tangential velocity vt is given as:

vt = r × ω

where, 

r is radius of the circular path
ω is angular velocity

ω = dθ/dt 
 = 2π/t

where,

dθ/dt is time rate change of angular displacement θ
t is time taken.

Thus, the tangential velocity becomes:

vt = r × dθ/dt

vt = r × 2π/t

The tangential velocity of any object moving in a circular direction can be calculated using the tangential velocity formula. 

Unit and Dimension of Tangential Velocity

Tangential Velocity is similar to normal velocity but is in the tangential direction. The unit of tangential velocity is Metre Per Second or m/s. It is measured using the formula,

vt = r × ω

The dimension formula for Tangential Velocity is [M0LT-1].

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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 m

Formula 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 m

Thus, radius of the wheel is 2 meters

FAQs on Tangential Velocity

Question 1: What is tangential velocity?

Answer:

Tangential velocity is the velocity of an object in tangential direction when it is performing circular motion at any given instant.

Question 2: How to find tangential acceleration from velocity?

Answer:

Tangential Acceleration is the rate of change of tangential velocity. It is calculated as,

at = vt / t

where,
at is the tangential acceleration
vt is the tangential velocity
t is the time taken

Question 3: What is the SI Unit of Tangential Velocity?

Answer:

The SI Unit of Tangential Velocity is m/s.

Question 4: What is the relation between Tangential Velocity and Angular Velocity?

Answer:

Tangential Velocity formula is given by the product of the radius of a circular path and the angular Velocity of the rotating object.

vt = r ω

where,
vt is the tangential velocity
r is the radius of the circular path
ω is the angular velocity



Last Updated : 04 Feb, 2024
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