Rotational Equations and Center of Mass

1. Rotational Equations and Center of Mass

2. Use one of the rotational constant acceleration equations. You have a wheel that starts at 10 rad/s. It accelerates with a rotational acceleration of -0.5  rad/s2. What is the magnitude of its angular displacement after 20 s?

3. You see four cars from an airplane. Being bored you derive an equation for each of their positions. The first is x(t) = 2t+5. The second is x(t) = -6t-4. The third is y(t) = 4t. The fourth is x(t) = -4 and y(t) = 7t+5. At time t = 0, what is the center of mass of the four car system?

4. You see four cars from an airplane. Being bored you derive an equation for each of their positions. The first is x(t) = 2t+5. The second is x(t) = -6t-4. The third is y(t) = 4t. The fourth is x(t) = -4 and y(t) = 7t+5. At time t = 2, what is the center of mass of the four car system?

5. You see four cars from an airplane. Being bored you derive an equation for each of their positions. The first is x(t) = 2t+5. The second is x(t) = -6t-4. The third is y(t) = 4t. The fourth is x(t) = -4 and y(t) = 7t+5. What is the speed of the center of the mass of this system?

6. A pole has a linear density of (0.3 x) kg/m. If it has a length of 200 cm, where is the center of mass from the lighter end of the bat?

7. Which of the following is the rotational counterpart of force? • q • w • a • I • t • K • L

8. What is the name of the variable t? • Angular Acceleration • Moment of Inertia • Torque • Rotational Kinetic Energy • Angular Momentum • Angular displacement (angle) • Angular velocity • Angular Force

9. What is the magnitude of the force that the ball is putting on the cross-beam? y x m = 200 kg

10. Given the board below and using the equation and assuming that the point of rotation is the one shown, what is the magnitude of the torque that the ball is putting on the cross-beam? y Point of rotation x 30o 10 m m = 200 kg

11. Given the board below and using the equation and assuming that • the point of rotation is the one shown, what is the direction of the torque • that the ball is putting on the cross-beam? • i 3. j 5. k • -i 4. -j 6. -k y Point of rotation x 30o 10 m m = 200 kg

12. What keeps the truck from flipping over? • The tension in the cable • The weight of the of the truck • The torque from the cable • The torque from the weight of the truck y Point of rotation x 30o 10 m m = 200 kg

13. What is the magnitude of the torque from the weight of the truck? y Point of rotation x 30o 10 m m = 200 kg

14. What is the direction of the torque from the weight of the truck? • i 3. j 5. k • -i 4. -j 6. -k y Point of rotation x 30o 10 m m = 200 kg

15. If the truck weight 2000 kg, how far is the center of mass of the truck from the center of rotation? y Point of rotation x 30o 10 m m = 200 kg

16. Adding 100 kg to the mass of the ball, we change the total torque. If the entire truck rotates with an acceleration of 5 rad/s2, what is its moment of inertia? y Point of rotation x 30o 10 m m = 200 kg

17. Using the moment of inertia from the last question and the angular acceleration of 5 rad/s2, what is the magnitude of the angular momentum of the truck after 10 seconds? y Point of rotation x 30o 10 m m = 200 kg

18. Using the moment of inertia from the last question and the angular acceleration of 5 rad/s2, what is the rotational kinetic energy of the truck after 10 seconds? y Point of rotation x 30o 10 m m = 200 kg

19. A spinning cue ball hits the eight ball in a game of billiards. Which of the following quantities are conserved? • Translational Velocity • Translational Momentum • Force • Translational Kinetic Energy • Angular Velocity • Angular Momentum • Torque • Rotational Kinetic Energy