1. Rotational Motion Equations & Examples An Original PowerPoint by Mr. Dewey

2. Axis of Rotation Theta=L/r360 = ? Radians Theta=L/r360 = ? Radians Omega = theta/t Omega = theta/t V=wr V=wr Alpha = omega/t Alpha = omega/t Video Video Video

3. Changing Angular Velocity Video Video Video What is a tan What is a tan What is a r What is a r a=a tan + a r a=a tan + a r This is a vector equation This is a vector equation Tubing Tubing Tubing

4. Constant Angular Acceleration In analogy to motion with constant linear acceleration: In analogy to motion with constant linear acceleration: Notice the similarity between linear (x, v, a) and angular () quantities and relationships Notice the similarity between linear (x, v, a) and angular () quantities and relationships

5. Rolling W/O Slipping V=rw V=rw

6. Torque = r x F = r F sin(theta ). = r x F = r F sin(theta ).

7. Rotational Inertia Sum torques = I x Alpha Sum torques = I x Alpha Sum torques = I x Alpha Sum torques = I x Alpha Rot Inertia Is not considered concentrated at the center of mass…mr 2. Rot Inertia Is not considered concentrated at the center of mass…mr 2. Page 208 Page 208

8. Rotational KE Work Done by Torque Work Done by Torque ½ Iw 2 ½ Iw 2 PE = ½ Iw 2 + ½ mv 2 PE = ½ Iw 2 + ½ mv 2 Sliding vs. Rolling Sliding vs. Rolling Sliding vs. Rolling Sliding vs. Rolling Disc vs. Hoop Disc vs. Hoop Disc vs. Hoop Disc vs. Hoop

9. Conservation of Angular Momentum Video Video Video L=Iw L=Iw Right Hand Rule Right Hand Rule

12. Last but not least