Announcements 1.Midterm 2 on Wednesday, Oct Material: Chapters Review on Tuesday (outside of class time) 4.I’ll post practice tests on Web 5.You are allowed a 3x5 inch cheat card 6.Go through practice exams & homework & class examples; understand concepts & demos 7.Time limit for test: 50 minutes

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!

Connected cylinders. Two masses m 1 (5 kg) and m 2 (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. (a)What will happen when the masses are released? (b)Find the velocity of the masses after they have fallen a distance of 0.5 m. (c)What is the angular velocity of the pulley at that moment? Black board example 11.5

Torque A force F is acting at an angle  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  on the lever 

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   = 80 °; the other pulls at the middle of wrench with the same force and at an angle   = 90 °. What is the net torque the two mechanics are applying to the screw?

Particle of mass m rotating in a circle with radius r. force F r to keep particle on circular path. force F t accelerates particle along tangent. Torque  and angular acceleration  Newton’s __________ law for rotation. Torque acting on particle is ________________ to angular acceleration  :

Work in rotational motion: Definition of work: Work in linear motion: Component of force F along displacement s. Angle  between F and s. Torque  and angular displacement .

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

Linear motion with constant linear acceleration, a. Rotational motion with constant rotational acceleration, 

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

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

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 ____________

Rolling motion of a particle on a wheel (Superposition of ________ and ___________ motion) Rolling Rotation Linear + =

Superposition principle: Rolling motion = Pure _________ + Pure _______ Rolling motion Kinetic energy of rolling motion:

Torque Angular momentum Angular momentum is conserved Chapter 11: Angular Momentum part 1 Reading assignment: Chapter Homework :(due Monday, Oct. 17, 2005): Problems:30, 41, 42, 44, 48, 53

Torque and the ______________ Thus far: Torque Torque is the _____________ between the force vector F and vector r

Torque and the vector product Definition of vector product: - The vector product of vectors A and B is the ___________. - C is _________________ to A and B - The __________________ of is C = A·B·sin  

Torque and the vector product Use the right hand rule to figure out the direction of C. - __________ is C (or torque  angular velocity , angular momentum L ) - _____________ finger is A (or radius r) - ____________ finger is B (or force F) 

Torque and the vector product Rules for the vector product. If A is ______ to B then.Thus, If A is _______ to B then  Magnitude of C = A·B·sin  is equal to area of ______________ made by A and B

Torque and the vector product Rules for the vector product (cont). 6. 

A force F = (2.00i j) 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 j). Black board example 12.2 HW 21 (a)What is the torque exerted on the object? (b)What is the magnitude and direction of the torque vector . (c)What is the angle between the directions of F and r?