Question

What is meant by angular velocity? Give a relation between linear speed and angular velocity of a body moving along a circular path.

Answer 1

Answer:

To calculate the speed and angular velocity of objects. ... Angular speed gives the rate at which the central angle swept out by the object changes as the object moves around the circle, and it is thus measured in radians per unit time. Linear speed is measured in distance units per unit time (e.g. feet per second).

Explanation:

example

Linear velocity

v

is equal to the angular speed

ω

times the radius from the center of motion

R

.

We can derive this relationship from the arclength equation

S

=

θ

R

where

θ

is measured in radians.

Start with

S

=

θ

R

Take a derivative with respect to time on both sides

d

S

dt

=

d

θ

dt

R

d

S

dt

is linear velocity and

d

θ

dt

is angular velocity

So we're left with:

v

=

ω