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# Tangential Velocity Formula

When a body is moving in circular path at a distance r from its center its velocity at any instant will be directed tangentially. This is what we call tangential velocity. In simple words the linear velocity at any instant is its tangential velocity.

Tangential Velocity Formula

Where, r is the radius of circular path and
$\omega$ is the angular velocity given as $\omega$

Hence the Tangential Velocity Formula is given by

If time taken t is only given then Tangential Velocity is calculated using formula

Tangential velocity formula is useful in calculating the tangential velocity of any given body moving in a circular path. It is expressed in meter per second (m/s).

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## Tangential Velocity Problems

Given are solved problems on tangential velocity which may be helpful for you.

### Solved Examples

Question 1: Calculate the tangential velocity in the below figure if the particle is moving from A to B in 5s.

Solution:

Given: Radius r = 50 cm = 0.5 m,
Angular velocity $\omega$ = 20 $\pi$
The tangential velocity is given by Vt = r $\omega$
= 0.5 $\times$ 20 $\times$ 3.142
= 31.42 m/s.

Question 2: Calculate the tangential velocity in the below figure if the particle is moving from A to B in 5s.

Solution:

The body is traveling from point A to B in 5s.  The total time required is $\frac{t}{2}$ = 5 s $\therefore$ t = 10 s.
The tangential velocity is given by Vt = $\frac{2 \pi r}{t}$
= $\frac{2 \times 3.142 \times 3}{10}$
= 1.88 m/s.

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