Question

Find the linear velocity of a point moving with uniform circular motion, if the point covers a distance s in the given amount of time t. s

Answer 1

Answer:

The linear velocity is represented by the following expression: $v = \frac{s}{t}$

Explanation:

From Rotation Physics we know that linear velocity of a point moving with uniform circular motion is:

$v = r\cdot \omega$ (Eq. 1)

Where:

$r$ - Radius of rotation of the particle, measured in meters.

$\omega$ - Angular velocity, measured in radians per second.

$v$ - Linear velocity of the point, measured in meters per second.

But we know that angular velocity is also equal to:

$\omega = \frac{\theta}{t}$ (Eq. 2)

Where:

$\theta$ - Angular displacement, measured in radians.

$t$ - Time, measured in seconds.

By applying (Eq. 2) in (Eq. 1) we get that:

$v = \frac{r\cdot \theta}{t}$ (Eq. 3)

From Geometry we must remember that circular arc ($s$), measured in meters, is represented by:

$s = r\cdot \theta$

$v = \frac{s}{t}$

The linear velocity is represented by the following expression: $v = \frac{s}{t}$