1. CIRCULAR & ROTATIONAL MOTION

2. CIRCULAR MOTION Uniform Circular Motion
period, T: time for one complete revolution, unit: s
speed is constant
v = 2pr/T (r: radius)
velocity is constantly changing (because direction is changing)

3. CIRCULAR MOTION centripetal acceleration ac = v2/r
the greater the speed, the greater the centripetal acceleration
the smaller the radius of the turn, the greater the centripetal acceleration
a centripetal acceleration requires a centripetal force

4. CIRCULAR MOTION centripetal force ΣFc = mv2/r
any force can be cause a net centripetal force: gravity (planets & moons), friction (car turning a corner), tension (ball on a string), etc. Σ

5. (a) 4 seconds (b) 3.14 m/s (c) 4.9 m/s2 (d) 245 N
A 50 kg child on a merry-go-round sits 2.0 m from the center and makes 2.0 complete revolution every 8 seconds. (a) Find the child's period. (b) Find the child's tangential speed. (c) Find the child's centripetal acceleration. (d) Find the centripetal force on the child.
(a) 4 seconds
(b) 3.14 m/s
(c) 4.9 m/s2
(d) 245 N   

6. Frames of reference
inside a turning object, there seems to be a centrifugal (center- fleeing) force pulling on objects
outside the turning object, we see objects inside move in a straight line (inertia), until they get pulled into the turn by centripetal force
centrifugal force only exists within the turning object’s frame of reference - it is a fictitious force

7. ROTATIONAL MOTION Rotational Motion: rotation around an internal axis
angle, q: how much an object has rotated,
unit: radian (rad)
2p rad = 360º = 1 revolution (rev)
angular velocity, w = Dq/t : rate of rotation, unit: rad/s
for any point on a spinning object:
v = wr
(when using this expression, w must be in RADIANS!!!!)
frequency: revolutions per second, unit: Hertz, Hz
1 Hz = 1 rev/s = 2p rad/s

8. (a) 2.88 radians (b) 66 seconds (c) 0.38 m/s (d) 1.5 N
A 42 kg child is riding a horse on the outside of a carousel. If the horse moves through an arc length of 11.5 m and the diameter of the carousel is 8.00 m, through what angular displacement does the child travel?  The carousel has an angular velocity of 0.9 rpm (revolutions per minute), determine the period of the carousel, and the tangential velocity of the child. Determine the centripetal force acting on the child.
(a) 2.88 radians
(b) 66 seconds
(c) 0.38 m/s
(d) 1.5 N