Advertisement Remove all ads

In U. C. M (Uniform Circular Motion), Prove the Relation V = W x R, Where Symbols Have Their Usual Meanings. - Physics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Answer in Brief

In U. C. M (Uniform Circular Motion), prove the relation `vec v = vec w xx vec r`, where symbols have their usual meanings.

 
 
Advertisement Remove all ads

Solution

Analytical method :
Consider a particle revolving in the anticlockwise sense along the circumference of a circle of radius r with centre O as shown.

Let

`vec omega`= angular velocity of the particle

`vec v`= linear velocity of the particle

`vec r`= radius of the particle

In the vector form, the linear dispalcement is

`vec (delta s) = vec (delta theta) times vec r`

Dividing both sides by `delta t` we get

`vec (delta s)/(delta t) = vec (delta theta)/(delta t) times vec r`

`lim_(delta t -> 0) vec (delta s)/(delta t) = lim_(delta t -> 0) vec (delta theta)/(delta t) times vec r`

`therefore vec(dS)/dt = vec(d theta)/(delta t) times vec r`

but

`vec(dS)/dt = vec v` = Linear velocity

`vec(d theta)/(delta t) = vec omega` = angular velocity

`therefore vec v = vec omega times vec r`

Concept: Uniform Circular Motion
  Is there an error in this question or solution?

APPEARS IN

Video TutorialsVIEW ALL [2]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×