1. Rotational Motion and the Law of Gravity
Chapter 7
Rotational Motion and the Law of Gravity

2. Radian measure
We use radian units to measure angles in angular displacement

3. Radian measure

4. Angular speed and angular acceleration
Angular position
Angle measured from the x axis, in radians

5. Angular speed and angular acceleration
Angular displacement
Angle measured from the x axis, in radians

6. Angular Velocity (ω) What is velocity? angular velocity (ω)
the rate of change of angular position
Units: radians per second (rad/s)
Counter clockwise is positive
Clockwise is negative
(V) tangential speed

9. Angular Acceleration
Rate of change of angular velocity

10. Angular Acceleration
Rate of change of angular velocity

12. Circular Motion Newton’s 1st Law Newton’s 2nd Law

13. Circular Motion
When an object travels in a circular path, its linear velocity aka tangential velocity is constantly changing
It doesn’t change in magnitude, but it is constantly changing direction.
Because of this, it is often referred to as tangential speed (vt)
Changing velocity is known as…
In order for acceleration to take place, a _______________ is needed.

14. Circular Motion
The net Force is directed in toward the center of the circle and is also known as a centripetal force (Fc)
That force causes an acceleration that is also directed in toward the center of the circle, centripetal acceleration (ac)
Fc = mac
ac = (vt)2/r

15. The application of rotational dynamics to the space program
weightlessness-in-space-video.htm

16. Cage of Death https://www.youtube.com/watch?v=L9aREQpcLGU
Draw a free body diagram of the bike on the side of the cage, label the forces acting on the bike
When the bikers are on the side of the wall, why don’t they slide down?
Draw a free body diagram of the bike on the top of the cage, label the forces
What holds the bikers to the top of the cage? Why don’t they fall down?

17. Climbing the walls… https://www.youtube.com/watch?v=5ITnzF9itKM
Draw a free body diagram of the runner going up a wall, label the forces
What enables the runner to go up the wall?
what stops the runners’ upward progress?
What rotational concepts are at play in limiting the runners’ upward progress?

18. Calculate Fg for an object of unknown mass at sea level (6,371 km) on the Earth (approx. 5.98x1024 kg)
Calculate Fg for an object of unknown mass at the top of the tallest mountain in the world, Mt Chomolungma (8,848 m above sea level)
What is the average of those two numbers?

21. Kepler’s Laws Kepler’s First Law
All planets move in elliptical orbits, with the sun at one focus.

22. Kepler’s Laws Kepler’s Second Law
A line that connects a planet to the sun sweeps out equal areas in equal times.
When the planet is closer to the sun, it moves faster, sweeping through a longer path in a given time.

23. Kepler’s Laws Kepler’s Second Law Fc = Fg = G (m1m2)/r2 ac = Fc/m
ac = vt2/r
vt = (acr)^1/2

24. Kepler’s Laws Kepler's third law
the law of harmonies - compares the orbital period and radius of orbit of a planet to those of other planets.

25. Kepler’s Laws Kepler's third law –
the law of harmonies - compares the orbital period and radius of orbit of a planet to those of other planets.

26. Kepler’s Laws Kepler's third law –
the law of harmonies - compares the orbital period and radius of orbit of a planet to those of other planets.

28. The motion of the Sun, Earth and planets simplified…