1. “If a 10 kg mass travels in a circle of 5 m radius, and experiences a centripetal acceleration of 3 m/s2, what would the acceleration be if the circle were 15 m in radius, and everything else stayed the same”

2. “If a 1000 kg mass travels in a circle of 50 m radius, and experiences a centripetal acceleration of 5 m/s2, what would the acceleration be if the object
lost half it’s mass, and everything else stayed the same”

3. Newton’s Law of Gravity
Wanted to explain Kepler’s work
Developed laws of motion en route to law of gravity
1665 speculated force that caused fall of apple kept Moon in its orbit
Orbiting is falling
Same laws of physics for Moon and Earth

4. Newton’s Law of Gravity
Newton compared accelerations
Acceleration  1/distance2
Accel (m/s2)
Dist. (m)
Ratio of acceleration
Ratio of dist.
Ratio2 of dist.
Moon
2.52 x 10-3
4.0 x 108
1/3896
62.5
3906
apple
9.8
6.38 x 106

5. Newton’s Law of Gravity
F  1/r2
Twice distance ¼ force
4 x distance /16 force
½ distance x force

6. Newton’s Law of Gravity
Galileo
Big & small bodies fall with same acceleration
Newton a = F/m
Same a means bigger F for bigger m
F  m F  m1 x m2

7. Newton’s Law of Gravity
Put them together
F  m1m2 r2
Equation F = Gm1m2
G is proportionality constant
G = 6.67 x N·m2/kg2

8. Gravitational Force
Earth (mE = 5.98 x 1024 kg) is x 1011 m from the the Sun (mS = 1.99 x 1030 kg)
What is the gravitational force?
3.55 x 1022 N

9. Centripetal Force
Earth (mE = 5.98 x 1024 kg) goes around the Sun in 1 year (365 days)
rorbit = x 1011 m
What centripetal force is required?

10. Centripetal Force F = mv2/r What is the average speed of the earth?
vA = xT/tT
What distance does the Earth travel (m)?
How long does it take to travel (s)?

11. Centripetal Force What is the average speed of anything? vA = xT/tT
What distance does the Earth travel (m)?
How long does it take to travel (s)?
What is the centripetal force (N)?

12. Weight Newton’s Second Law W = mg
What is the weight force of a 70 kg person standing on the Earth?

13. Weight of 70 kg person
70 kg
686 N
9.8 m/s2

14. Gravitational Force
For spherical objects the law of gravity behaves as if all the mass is concentrated at a tiny point at the center of the sphere

15. Gravitational Force
A person (70 kg) is standing on the surface of the Earth (mE = 5.98 x 1024 kg, rE = 6.38 x 106 m)
From Newton’s Law of Gravity
F = Gm1m2 r2
What is the gravitational force between the person and the Earth?

16. Gravitational force between person and Earth
4.38 x 109 N
3.5 x 105 N
8.23 x N
686 N

17. Newton’s Law of Gravity
Results
Gravitational acceleration
independent of mass
Depends only on distance
Why projectile motion is parabola
F = ma  with g & r can calculate mass

18. Rotational Motion and Torque

19. Rotational Motion & Quantities
In angular motion physical results depend on the distance from the axis of rotation

20. Rotational Motion & Quantities
In a rotating CD all the parts complete a revolution in the same time
Bits further from the center must move faster
Bigger circumference; same time

21. Angular Measure
Angle defined as arc length divided by radius

22. Radians Number of radians = arc length/radius = s/r
Length around circle = 2pr
Radius of circle = r
2p radians in a circle
Conversion: radians to degrees 180º/p

23. Rotational Motion Quantities
Quantities based on motion
q – angular distance
w – angular velocity
a – angular acceleration
t – time

24. Equations of Linear Motion
x = vt
a = (v – vo)/t = Dv/Dt
v = vo + at
va = (v + vo)/2
x = vot + ½ at2
v2 = vo2 + 2ax
q = wt
a = (w – wo)/t = Dw/Dt
w = wo + at
wa = (w + wo)/2
q = wot + ½ at2
w2 = wo2 + 2aq