1. Rotation Energy Examples Kinetic Energy ( E k ) - The ability to produce change due to an object’s motion. Linear Kinetic EnergyRotational Kinetic Energy

2. Rotation Energy Examples 1.A 5.0 kg mass is hung from a massless rope which is tied around a pulley that can be approximated as a hoop of mass 4.0 kg and radius 0.25 m. The rope does not slip, and there is no friction in the system. a.What is the acceleration of the falling mass? m M, R But

3. Rotation Energy Examples 1.A 5.0 kg mass is hung from a massless rope which is tied around a pulley that can be approximated as a hoop of mass 4.0 kg and radius 0.25 m. The rope does not slip, and there is no friction in the system. a.What is the acceleration of the falling mass? m M, R m So that m accelerates downward

4. Rotation Energy Examples 1.A 5.0 kg mass is hung from a massless rope which is tied around a pulley that can be approximated as a hoop of mass 4.0 kg and radius 0.25 m. The rope does not slip, and there is no friction in the system. a.What is the acceleration of the falling mass? m M, R m So that m accelerates downward But

5. Rotation Energy Examples 1.A 5.0 kg mass is hung from a massless rope which is tied around a pulley that can be approximated as a hoop of mass 4.0 kg and radius 0.25 m. The rope does not slip, and there is no friction in the system. a.What is the acceleration of the falling mass? m M, R m So that m accelerates downward

6. Rotation Energy Examples 1.A 5.0 kg mass is hung from a massless rope which is tied around a pulley that can be approximated as a hoop of mass 4.0 kg and radius 0.25 m. The rope does not slip, and there is no friction in the system. b.What is the tension in the rope?

7. Rotation Energy Examples 1.A 5.0 kg mass is hung from a massless rope which is tied around a pulley that can be approximated as a hoop of mass 4.0 kg and radius 0.25 m. The rope does not slip, and there is no friction in the system. c.What is the angular acceleration of the pulley?

8. Rotation Energy Examples 1.A 5.0 kg mass is hung from a massless rope which is tied around a pulley that can be approximated as a hoop of mass 4.0 kg and radius 0.25 m. The rope does not slip, and there is no friction in the system. d.What is the pulley’s angular velocity at 1.5 s ?

9. Rotation Energy Examples 1.A 5.0 kg mass is hung from a massless rope which is tied around a pulley that can be approximated as a hoop of mass 4.0 kg and radius 0.25 m. The rope does not slip, and there is no friction in the system. e.What is the pulley’s kinetic energy at 1.5 s ?

10. Rotation Energy Examples 2.A rigid body is made of three identical thin rods, each with length l, fastened together in the form of a letter H. The body is allowed to fall from rest from a position in which the plane of the H is horizontal. a.What is the rotational inertia of the H? Since rod 1 has no radius Since rod 2 is a thin rod rotated about one end Since rod 3 acts like a hoop with all mass a distance l away from the axis of rotation

11. Rotation Energy Examples 2.A rigid body is made of three identical thin rods, each with length l, fastened together in the form of a letter H. The body is allowed to fall from rest from a position in which the plane of the H is horizontal. b.What is the angular speed of the body when the plane of the H is vertical?? Use the Law of Conservation of Energy Must use the center of mass to determine y i

12. Rotation Energy Examples 2.A rigid body is made of three identical thin rods, each with length l, fastened together in the form of a letter H. The body is allowed to fall from rest from a position in which the plane of the H is horizontal. b.What is the angular speed of the body when the plane of the H is vertical?? Must use the center of mass to determine y i