2. Help Session
November 12th
MAP PM
SPECIAL OFFICE HOURS:
Tuesday: 11AM-1PM

3. Uniform circular motion is due to a centripetal acceleration
This acceleration is always pointing to the center
This acceleration is due to a net force
arad = v2/R

4. A diagram of gravitational force

5. We want to place a satellite into circular orbit 300km above the earth surface.
What speed, period and radial acceleration it must have?

6. What is “work” as defined in Physics?
Formally, work is the product of a constant force F through a parallel displacement s.
W is N.m
W = F.s
1 Joule (J) = (1N.m)

7. W > 0
W < 0
W = 0

8. Work and Kinetic Energy work-energy theorem
W = Kf - Ki

9. Gravitational Potential Energy (Near Earth’s surface)
U = mgy

10. Uel = (1/2) kx2

11. Work-Energy Theorem
Wtotal = Kf – Ki
Conservatives force
Kf + Uf = Ki + Ui
Non-conservative forces
Kf + Uf = Ki + Ui + Wother

13. Off center collisions

14. Suppose we have several particles A, B, etc. , with masses mA, mB, …
Suppose we have several particles A, B, etc., with masses mA, mB, …. Let the coordinates of A be (xA, yA), let those of B be (xB, yB), and so on. We define the center of mass of the system as the point having coordinates (xcm,ycm) given by
xcm = (mAxA + mBxB + ……….)/(mA + mB + ………),
Ycm = (mAyA + mByB +……….)/(mA + mB + ………).

16. v = rω
atan = rα
arad = rω2

17. Kinetic Energy of Rotating Rigid Body Moment of Inertia
KA = (1/2)mAvA2
vA = rA ω vA2 = rA2 ω2
KA = (1/2)(mArA2)ω2
KB = (1/2)(mBrB2)ω2
KC = (1/2)(mCrC2)ω2 ..
K = KA + KB + KC + KD ….
K = (1/2)(mArA2)ω2 + (1/2)(mBrB2)ω2 …..
K = (1/2)[(mArA2) + (mBrB2)+ …] ω2
K = (1/2) I ω2
I = mArA2 + mBrB2 + mCrC2) + mDrD2 + …
Unit: kg.m2

19. Rotation about a Moving Axis
Every motion of of a rigid body can be represented
as a combination of motion of the center of mass (translation) and rotation about an axis through the center of mass
The total kinetic energy can always be represented as the sum of a part associated with motion of the center of mass (treated as a point) plus a part asociated with rotation about an axis through the center of mass

20. Ktotal = (1/2)Mvcm2 + (1/2)Icmω2
Total Kinetic Energy
Ktotal = (1/2)Mvcm2 + (1/2)Icmω2

23. Rotation about a moving axis

24. Conservation of angular momentum
When the sum of the torques of all external
forces acting on a system is zero, then
THE TOTAL ANGULAR MOMENTUM IS CONSTANT (CONSERVED)

25. The professor as figure skater?
It seems that danger to the instructor is proportional to interest in any given demonstration.