# Tangential Velocity Formula

## Tangential Velocity Formula

Any object moving along a circular path has a linear component to its speed called tangential velocity. An object’s velocity is always pointed tangentially when it travels in a circle at a distance r from the centre. Tangential velocity is the name given to this. Additionally, we can state that the linear velocity is always the tangential velocity. This is the base of Tangential Velocity Formula.

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### What is Tangential Velocity?

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Simply put, a tangent is a line that only ever touches one point of a non-linear curve, such as a circle. On a two-dimensional graph, it shows an equation describing the relationship between the coordinates “x” and “y.”

The measurement of speed at any point parallel to a rotating wheel in a circular motion is known as the tangential velocity. Thus, the tangential velocity, Vt, and the angular velocity,, are related by the formula. The part of motion along a circle’s edge that can be measured at any given time is called tangential velocity. Tangential velocity, as suggested by its name, refers to the motion of an object along the circumference of a circle, with its direction at any given point always being along the tangent to that point.

### The Formula for Tangential Velocity

To begin, we must compute the angular displacement, which is the ratio of the length of the arc’s’ traced by an object on this circle to its radius ‘r’. It is measured in radians.

The rate of change of the object’s angular displacement is its angular velocity. It is denoted by ω and its standard unit is radians per second.

It differs from linear velocity in that it only applies to objects moving in a circular motion. As a result, it determines the rate at which angular displacement is swept.

Tangential Velocity Formula is: Vt=r×dθdt

Tangential Velocity Formula can also be: Vt=r×ω

Another formula for Tangential Velocity is: Vt=2πrt

Where,

Vt Tangential Velocity

r The radius of the circular path

ω Angular Velocity

t Time

θ Angular Displacement

Tangential velocity formula is applicable in calculating the tangential velocity of any object moving in a circular path. Its unit is meter per second.

Solved Examples for Tangential Velocity Formula

Q.1: If the angular velocity of a wheel is 40 \frac{rad}{s}, and the wheel diameter is 60 cm. Determine the tangential velocity of the wheel.

Solution: Given parameters are,

r=12×60

r= 30 cm

r = 0.30 m.

Tangential velocity formula is as given:

Vt=r×ω

=0.30×40

= 12 m/s

Thus tangential velocity will be 12 meters per sec.

Q.2: If a wheel is turning with a speed of 12 m per sec, and its angular velocity is 6 radians per sec. Then find out its radius.

Solution: The tangential velocity is as follows,

Vt=12mpersec.

The angular velocity, ω, is 6 radians/sec.

Now the formula for tangential velocity is:

Vt=r×ω

Rearranging it,

r=Vtω

=126

= 2 m

Therefore, the radius is 2 meters.