Join TSR now and get all your revision questions answeredSign up now

circular motion - how to prove/derive v=rw? Watch

    • Thread Starter
    Offline

    1
    ReputationRep:
    title says it all
    Offline

    2
    ReputationRep:
    You're moving in a circle of radius r, so the distance you travel in one full trip round the circle is 2.pi.r and you're doing it in one time period, T

    speed, v = distance/time = 2.pi.r/T

    w = angular speed, and you complete 2 pi radians in time T, so w = 2pi/T

    so v=rw
    • Thread Starter
    Offline

    1
    ReputationRep:
    Thankyou!

    you can have a little dribble of green tomorrow! (alredy repped today ) :p:
    Offline

    2
    ReputationRep:
    Heh, thankyou muchly I shall look forward to it :p:
    Offline

    1
    ReputationRep:
    or you could use calculus to prove it:

     S = r \theta \to \frac{d S}{dt} = \frac{d (r \theta)}{dt} = r \frac{d \theta}{dt} + \theta \frac{d r}{dt}

    If your moving on a circle, your radius is not changing with time so  \frac{dr}{dt} = 0

    so  v = \frac{dS}{dt} = r \frac{d \theta}{dt} = r \omega
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by div curl F = 0)
    or you could use calculus to prove it:

     S = r \theta \to \frac{d S}{dt} = \frac{d (r \theta)}{dt} = r \frac{d \theta}{dt} + \theta \frac{d r}{dt}

    If your moving on a circle, your radius is not changing with time so  \frac{dr}{dt} = 0

    so  v = \frac{dS}{dt} = r \frac{d \theta}{dt} = r \omega
    ahhh clever!
 
 
 
Poll
How are you feeling about Results Day?

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.