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

Physics and electronics discussion, revision, exam and homework help.

Announcements Posted on
Please change your TSR password 23-05-2013
Enter our travel-writing competition for the chance to win a Nikon 1 J3 camera 20-05-2013
IMPORTANT: You must wait until midnight (morning exams)/4.30AM (afternoon exams) to discuss Edexcel exams and until 1pm/6pm the following day for STEP and IB exams. Please read before posting, including for rules for practical and oral exams. 28-04-2013
Search Thread
Advanced Search
Sign in to Reply
  1. amjw's Avatar
    1 09-12-2007  17:11
    • Exalted and Worshipped Member
    • Posts: 1,236
    circular motion - how to prove/derive v=rw?
    title says it all
  2. -G-a-v-'s Avatar
    2 09-12-2007  18:56
    • Vengeful, Imperial Overlord of The Student Room
    • Location: Stoke-on-Tremt
    • Posts: 3,971
    Re: circular motion - how to prove/derive v=rw?
    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
  3. amjw's Avatar
    3 09-12-2007  19:37
    • Exalted and Worshipped Member
    • Posts: 1,236
    Re: circular motion - how to prove/derive v=rw?
    Thankyou!

    you can have a little dribble of green tomorrow! (alredy repped today ) :p:
  4. -G-a-v-'s Avatar
    4 09-12-2007  21:42
    • Vengeful, Imperial Overlord of The Student Room
    • Location: Stoke-on-Tremt
    • Posts: 3,971
    Re: circular motion - how to prove/derive v=rw?
    Heh, thankyou muchly I shall look forward to it :p:
  5. div curl F = 0's Avatar
    5 10-12-2007  09:01
    • Peer Of The TSR Realm
    • Location: Chester
    • Posts: 1,604
    Re: circular motion - how to prove/derive v=rw?
    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
  6. amjw's Avatar
    6 10-12-2007  15:47
    • Exalted and Worshipped Member
    • Posts: 1,236
    Re: circular motion - how to prove/derive v=rw?
    (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!
Sign in to Reply
Search Thread
Advanced Search
Share this discussion:  
Useful resources

Articles:

Study Help rules and posting guidelinesStudy Help Member of the Month nominationsGuide to PhysicsPhysics revision notes in the TSR wikiIndex of useful Physics threadsPhysics resourcesPhysics websitesPhysics textbook reviewsRecommended Physics reading

Quick Link:

Unanswered Physics Threads

Groups associated with this forum:

View associated groups
Article updates
Moderators

We have a brilliant team of more than 60 volunteers looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is moderated by:

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

Shortcuts

Get Started

TSR Group

Using TSR

Info

Connect with TSR

Reputation gems:
The Reputation gems seen here indicate how well reputed the user is, red gem indicate negative reputation and green indicates a good rep.
Post rating score:
These scores show if a post has been positively or negatively rated by our members.