1. Momentum principle
The change in momentum of a body is equal to the net force acting on the body times (乘) the duration of the interaction.

2. Angular momentum principle
The change in angular momentum of a body (around a given point) is equal to the net torque acting on the body (around the same point) times (乘) the duration of the interaction.

3. Angular momentum principle
Greek letter “tau”
Instantaneous version:
where is the torque (力矩) around the point A.

4. Newton’s 2nd Law for rotation of a
rigid body A
(this step assumes the body is planar or symmetrical)
Total torque due to external forces.

5. Example: A lever (杠杆) + A

6. Example: A lever (杠杆) + A
Newton’s 2nd law:

7. Example: A lever (杠杆) + A
If the lever is balanced, α = 0, so:

8. Example: A yo-yo (溜溜球)
A yo-yo (assumed to be a cylinder) has mass M and radius R. Find its downward acceleration, and the tension force in the string Ft.

9. Homework:
In a ‘real’ yo-yo, the string is wrapped around an axle with radius r < R. What is the advantage of this design?
HINT: Assume the moment of inertia is the same as for a cylinder of radius R. How does the torque change?

10. Example: A bowling ball, rolling down a ramp
Momentum principle, x direction:

11. Example: A bowling ball, rolling down a ramp
Angular momentum principle, around center of mass (vectors along z axis):
Substitute into momentum equation
Compare to sliding.