1. Rotational Motion AP Physics C

2. Introduction The motion of a rigid body (an object with a definite shape that does not change) can be analyzed as the translational motion of its center of mass AND the rotational motion about its center of mass. All points on a rotating rigid body move in circles and the center of these circles lie on a line called the axis of rotation

3. Axis of Rotation

4. Angular Displacement –Symbol: θ –Unit: radian, rad –360° = 2π radians –1 rad = 57.3°

5. Angular Velocity –Symbol: ω –Unit: rad/s –Direction Every point on a rotating rigid body has the same ω

6. Angular Acceleration –Symbol: α –Unit: rad/s 2 –Direction Every point on a rotating rigid body has the same α

7. Angular Acceleration

8. Angular & Linear Analogies Δθ ω α ΔxvaΔxva In rotational motion if you know the analogous quantity in the linear realm all you do is replace the linear quantity with the angular quantity and you have the angular equation

10. Relating Angular to Linear

12. Kinetic Energy Will K = ½mv 2 work in order to calculate the energy of a solid rotating disk? v = rω K = ½ m(rω) 2

13. Moment of Inertia aka Rotational Inertia The tendency of a body to resist a rotation Page 278 for various shapes. Unit: kgm 2

14. Rotational Kinetic Energy This is not a new form of energy, rather it is the sum of the individual kinetic energies of the individual particles of the rigid body written in a compact and convenient form.

15. Energy is still conserved

16. Center of mass Define Locations for various shapes: cube, bowling ball, basketball, donut, people Stability: tightrope walkers, getting low Pole and wine glass demo.

17. Parallel Axis Theorem The moment of inertia for an axis through the center of mass is lower than for any parallel axis

18. Moment of Inertia with Calculus

19. Chapter 10 Dynamics of Rotational Motion Chapter 10 Q# 5, 7, 9, 15 & 22 P# 2, 3, 11, 12, 25, 27, 29, 33, 55, 58, 60, 74 & 81

20. Rotational Dynamics: What causes rotational motion? An applied force causes motion therefore an applied force is necessary to make a body rotate but where that force is applied will also determine the rotation of the body

21. Torque The quantitative measure of the tendency of a force to cause or change the rotational motion of a body. “Angular force” Unit: m N

22. Magnitude of Torque lever arm vs F ┴

23. Rotational analogy for Newton’s 2 nd Law (rigid bodies only)

24. Work and Power in Rotational Motion

25. Angular Momentum Unit: kgm 2 /s

26. Lazy Susan Demo

27. Newton’s 2 nd Law’s Rotational Analog in terms of angular momentum

28. Now the pulley has mass!! Atwood machine and pulley has mass.