1. PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

2. Circular Motion
Rotation
Revolution

3. 3 Different Kinds of Speed
1. Linear Speed - covering a distance in a time. S=D/t
2. Tangential Speed - speed of something moving in a circular path.
V = 2πr/T (Revolving!)
3. Rotational Speed - the number of rotations in a second. Sr= # rot./ second
Come up with an example of each.

4. 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)

5. CIRCULAR MOTION
all turning objects have centripetal acceleration (toward the center of the turn)

6. 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

7. CIRCULAR MOTION
no centripetal force = no turning (linear motion)

8. CIRCULAR MOTION centripetal force, Fc = mv2/r
Any force can be a centripetal force: gravity (planets & moons), friction (car turning a corner), tension (ball on a string), etc.

9. CIRCULAR MOTION
Frames of Reference - inside a turning object, there seems to be a centrifugal (outward from the center) force pulling on objects

10. CIRCULAR MOTION
Frames of Reference - outside the turning object, we see objects inside move in a straight line (following Newton’s 1st Law), until they get pulled into the turn by centripetal force

11. CIRCULAR MOTION
centrifugal force only exists within the turning object’s frame of reference - it is a fictitious force

12. CIRCULAR MOTION
Frames of Reference - things moving on a rotating object seem to be made to turn by the “coriolis force”

13. QUIZ 3.1
A child on a merry-go-round sits 1.5 m from the center and makes 2.0 complete revolutions every second.
(a) Find the child's period.
(b) Find the child's speed.
(c) Find the child's centripetal acceleration.   
v = 2pr/T ac = v2/r Fc = mv2/r

14. UNIT 3: CIRCULAR & ROTATIONAL MOTION
PHYSICS
UNIT 3: CIRCULAR & ROTATIONAL MOTION

15. UNIVERSAL GRAVITATION
Newton's Law of Universal Gravitation: masses attract
gravity force is proportional to each mass
twice the mass = twice the force
gravity force is inversely proportional to the square of the distance between the masses
twice the distance = ¼ the force
distance measured from center of mass: point on a body around which mass is balanced

16. UNIVERSAL GRAVITATION
Newton's Law of Universal Gravitation:
Fg = Gm1m2/r2
Fg: force of gravity, m: mass, r: distance between masses
G: universal gravitational constant, 6.67×10-11 Nm2/kg2
gravity is only significant for very large masses

17. UNIVERSAL GRAVITATION
acceleration due to gravity, g = Gme/r2
me: earth's mass (5.97×1024 kg)
r: distance from earth’s center (6.38×106 m + altitude)
g is only 9.80 m/s2 at sea level – it decreases as altitude increases
g is different on other planets & moons (it depends on the planet’s mass and radius)

18. UNIVERSAL GRAVITATION
Orbits: gravity provides the centripetal force
stable orbit: Fc = Fg
orbit speed v = √Gme/r
orbit period T = 2pr/v
geosynchronous orbit: T = 24.0 hrs, satellite stays over same position on earth

19. UNIVERSAL GRAVITATION
Orbits
always falling but never reaching the ground
"Weightlessness" is NOT gravity-less
no gravity = no orbit
weightless is no normal force

20. UNIT 3: CIRCULAR & ROTATIONAL MOTION
PHYSICS
UNIT 3: CIRCULAR & ROTATIONAL MOTION

21. 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
frequency: revolutions per second, unit: Hertz, Hz
1 Hz = 1 rev/s = 2p rad/s

22. ROTATIONAL MOTION Rotational Motion & Circular Motion
angular acceleration, a= Dw/t: rate of change in rotation, unit: rad/s2
Rotational Motion & Circular Motion
for any point on a spinning object:
v = rw
ac = rw2

23. ROTATIONAL MOTION torque, t: rotating effect of a force, unit: Nm
t = Fdsinq
d: "torque arm" or "lever arm“
q: angle between F and d
torque direction: clockwise (c) or counterclockwise (cc)

24. ROTATIONAL MOTION Torque is zero when q = 0º or 180º
Torque is maximum when q = 90º

25. ROTATIONAL MOTION Newton's Laws for Rotary Motion
A spinning object keeps spinning with constant angular velocity unless a net torque acts on it
A net torque causes an angular acceleration
For every action torque, there is an equal and opposite reaction torque

26. ROTATIONAL MOTION
Rotational Equilibrium: object is balanced, or moves with constant angular velocity, due to no net torque
Stc = Stcc F1 F2 d1 d2
F2d2 = F1d1

27. UNIT 3: CIRCULAR & ROTATIONAL MOTION
PHYSICS
UNIT 3: CIRCULAR & ROTATIONAL MOTION

28. UNIT 3 REVIEW v = 2pr/T ac = v2/r Fc = mv2/r
Fg = Gm1m2/r2 G = 6.67×10-11 Nm2/kg2
g = Gmp/r2 v = √Gmp/r
me = 5.97×1024 kg re = 6.38×106 m
w = Dq/t a= Dw/t
v = rw ac = rw2
t = Fdsinq Stc = Stcc