Announcements Midterm 2 on Wednesday, Oct. 19. Material: Chapters 7-11 Review on Tuesday (outside of class time) I ll post practice tests on Web

**Title: Announcements** ** 1**Announcements Midterm 2 on Wednesday, Oct. 19. Material Chapters 7-11 Review on Tuesday (outside of class time) Ill post practice tests on Web You are allowed a 3x5 inch cheat card Go through practice exams homework class examples understand concepts demos Time limit for test 50 minutes ** 2** Conservation of energy (including rotational energy) Again If there are no non-conservative forces Energy is conserved. Rotational kinetic energy must be included in energy considerations!

** 3** Black board example 11.5 Connected cylinders.

Two masses m1 (5 kg) and m2 (10 kg) are hanging from a pulley of mass M (3 kg) and radius R (0.1 m), as shown. There is no slip between the rope and the pulleys. What will happen when the masses are released?Find the velocity of the masses after they have fallen a distance of 0.5 m. What is the angular velocity of the pulley at that moment? ** 4** Torque f A force F is acting at an angle f on a lever that is rotating around a pivot point. r is the ______________ between F and the pivot point. This __________________ pair results in a torque t on the lever

** 5** Black board example 11.6 Two mechanics are trying to open a rusty screw on a ship with a big ol wrench. One pulls at the end of the wrench (r 1 m) with a force F 500 N at an angle F1 80 the other pulls at the middle of wrench with the same force and at an angle F2 90 . What is the net torque the two mechanics are applying to the screw?

** 6** Torque t and angular acceleration a. Newtons __________ law for rotation. Particle of mass m rotating in a circle with radius r. force Fr to keep particle on circular path. force Ft accelerates particle along tangent. Torque acting on particle is ________________ to angular acceleration a

** 7** Definition of work Work in linear motion Component of force F along displacement s. Angle g between F and s. Work in rotational motion Torque t and angular displacement q.

** 8** Work and Energy in rotational motion Remember work-kinetic energy theorem for linear motion External work done on an object changes its __________ energy There is an equivalent work-rotational kinetic energy theorem External, rotational work done on an object changes its _______________energy

** 9** Linear motion with constant linear acceleration, a. Rotational motion with constant rotational acceleration, a.

** 10** Summary Angular and linear quantities Linear motion Rotational motion Kinetic Energy Kinetic Energy Torque Force Momentum Angular Momentum Work Work

** 11** Rolling motion Pure rolling There is no ___________ Linear speed of center of mass

** 12** Rolling motion The _______ __________ of any point on the wheel is the same. The linear speed of any point on the object changes as shown in the diagram!! For one instant (bottom), point P has _______ linear speed. For one instant (top), point P has a linear speed of ____________

** 13** Rolling motion of a particle on a wheel (Superposition of ________ and ___________ motion) Rolling Rotation Linear

** 14** Rolling motion Superposition principle Rolling motion Pure _________ Pure _______ Kinetic energy of rolling motion

** 15** Chapter 11 Angular Momentum part 1 Reading assignment Chapter 11.4-11.6 Homework (due Monday, Oct. 17, 2005) Problems 30, 41, 42, 44, 48, 53

Torque Angular momentum Angular momentum is conserved ** 16** Torque and the ______________ Thus far Torque Torque is the _____________ between the force vector F and vector r

** 17** Torque and the vector product Definition of vector product f

- The vector product of vectors A and B is the ___________. C is _________________ to A and B The __________________ of is C ABsinf ** 18** Torque and the vector product f

Use the right hand rule to figure out the direction of C. __________ is C (or torque t, angular velocity w, angular momentum L) _____________ finger is A (or radius r) ____________ finger is B (or force F) ** 19** Torque and the vector product f Rules for the vector product. 1. 2. 3. 4. 5. Magnitude of C ABsinq is equal to area of ______________ made by A and B If A is ______ to B then . Thus, If A is _______ to B then

** 20** Torque and the vector product f Rules for the vector product (cont). 6.

** 21** Black board example 12.2 HW 21 A force F (2.00i 3.00j) is applied to an object that is pivoted about a fixed axis aligned along the z-axis. The force is applied at the point r (4.00i 5.00j).

What is the torque exerted on the object? What is the magnitude and direction of the torque vector t. What is the angle between the directions of F and r?