Question

Derive an expression for relation between linear velocity and angular velocity of a body moving in uniform circular motion.

Answer 1

What is Linear Velocity?

Linear and angular velocities are related to the speed of an object based on the perspective chosen. Linear velocity is applied to an object that moves, whereas angular velocity applies to those that turn such as a wheel, the earth’s revolution or a spinning top.

Angular Velocity to Linear Velocity

Anything that moves or turns in the circular direction has both linear velocity and angular velocity. The angular velocity is the ratio of the angle traversed to the amount of time it takes to traverse that angle.

Angular velocity gives an expression of angular displacement  over time and can be expressed in radians or degrees. Angular velocity is determined with the equation . To calculate the linear velocity from angular velocity, you can apply the formula , where ω is expressed in radians/time, and r indicates the radius of the path taken.

Constant Linear Velocity:

When a body moves with constant speed without changing its direction, it is said to be moving with the constant linear velocity. Linear velocity indicates the direction is not changed, and constant shows that the magnitude is not changed.

Formula:

The linear velocity depends on the distance traveled by an object with respect to time taken. The linear equation or the linear formula is given by,

v = x/t

Where,

v = Linear velocity

x = distance covered

t = Time taken to cover the distance(x).

i hope it will help you