Tangential Velocity Formula
Last Updated : 08 Apr, 2025
Tangential velocity refers to the linear speed of an object moving along a circular path. It is the velocity measured at any point tangent to the path of the object. In other words, it is the speed at which an object is moving along the circumference of a circle.
In this article, we will learn what Tangential velocity is, its formula, solve some examples.
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.
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.
.png)
Mathematically, the tangential velocity vt is given as:
vt = r × ω
where,
- r is Radius of 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].
Read, More
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
Worksheet: Tangetial Velocity
Problem 1: A point on the circumference of a rotating drum with a radius of 0.75 meters has a tangential velocity of 5 m/s. Calculate the angular velocity of the drum.
Problem 2: A point on the edge of a rotating disk has an angular velocity of 2 rad/s. If the radius of the disk is 0.5 m, calculate the tangential velocity of the point.
Problem 3: A car is traveling around a circular track with a radius of 100 meters. If the car has a tangential velocity of 20 m/s, what is its angular velocity?
Problem 4: A satellite orbits Earth with a radius of 7000 km and an angular velocity of 0.001 rad/s. Find the tangential velocity of the satellite.
Problem 5: A cyclist moves along a circular track with a radius of 25 m. If the cyclist's tangential velocity is 5 m/s, determine the cyclist's angular velocity.
Problem 6: The second hand of a clock is 0.1 meters long and completes one revolution every 60 seconds. What is the tangential velocity of the tip of the second hand?
Problem 7: An object moves with an angular velocity of 3 rad/s along a circular path with a radius of 2 meters. Calculate its tangential velocity.
Problem 8: A wheel with a radius of 0.4 meters rotates at 10 rad/s. What is the tangential velocity at the edge of the wheel?
Also, Read: