# Circular Motion Unit 1 Mod. 1 A2 OCR

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- Created by: Captain Jack Sparrow
- Created on: 18-06-13 17:49

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- Circular Motion
- Distance of one complete 'travel' around circle
- 2?r
- Circumference of circle

- 2?r
- Orbital Speed
- s = d/t
- d = 2?r
- 2?r = distance (around circle)
- v = 2?r/t

- 2?r = distance (around circle)
- s = v
- v = velocity
- v = 2?r/t

- v = velocity
- t = t
- t = time taken for travel

- t = time taken for travel

- d = 2?r

- s = d/t
- Angular Speed
- Ø = x/r
- Ø = Theta Radians (angle size in radians)
- Remember: 2? = 360°

- Ø = Theta Radians (angle size in radians)
- Angular speed - w
- w - omega (a little bit curvier in handwriting)
- w = 2?/t
- Radians per second
- "Amount of turn/ distance" per second - hence speed

- Simplifies to
- v = wr
- Proof
- v = 2?r/t
- Orbital Speed
- w = 2?/t
- "plugging in" w = 2?/t to v = 2?r/t
- v = wr

- "plugging in" w = 2?/t to v = 2?r/t

- v = 2?r/t

- Proof

- v = wr

- Radians per second

- w = 2?/ T
- Derived from
- f = w/2?
- 1/f = 2?/w
- T = 2?/w
- Rearranges to...
- w = 2?/T

- Rearranges to...

- T = 2?/w

- 1/f = 2?/w

- f = w/2?

- Derived from

- Ø = x/r
- Frequency
- f = w/2?
- f = frequency
- w = angular speed
- 2? = distance around whole circle

- f = w/2?
- Period
- TIME for ONE COMPLETE CYCLE
- T = 1/f
- Same as waves at AS - level

- Centripetal Acceleration
- dØ = dx/r
- Just the radian "rule" don't worry!

- v = dx/dt
- IMPORTANT: Only applies when dØ is VERY SMALL

- a = v^2/r
- a = w^2/r

- dØ = dx/r
- Centripetal Force
- F = mv^2/r

- Distance of one complete 'travel' around circle

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