1. PHYSICS UNIT 3: 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
all turning objects have centripetal (center- seeking) acceleration

4. 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

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

6. 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.

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

8. CIRCULAR MOTION
Frames of Reference - outside the turning object, we see objects inside move in a straight line (inertia), until they get pulled into the turn by centripetal force

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

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

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

12. QUIZ 3.1 A 50 kg child on a merry-go-round sits 2.0 m
from the center and makes 2.0 complete revolution
every second.
(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.   
v = 2pr/T ac = v2/r Fc = mv2/r

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

14. 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

15. 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

16. UNIVERSAL GRAVITATION
acceleration due to gravity, g = Gme/r2
Also known as the gravitational field strength
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)

17. 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

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

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

20. 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

21. 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

22. 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)

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

24. 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

25. 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

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

27. 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