Physics Announcements WebAssign – –Chapter 7 due today Exam #2 not graded yet Picture: 30-m Darrieus Wind turbine in the Magdalen Islands

Class Schedule 2/19Chapter 7Energy, Part 1 (Pg ) 2/21Chapter 7Energy, Part 2 (Pg ) 2/26Mid-term Exam #2 2/28Chapter 8Rotational Motion, Part 1 (Pg ) 3/5Chapter 8Rotational Motion, Part 2 (Pg ) 3/7Chapter 9Gravity (Pg ) 3/11 – 3/18 Spring Recess

Chapter 8 Rotational Motion, Part 1 Circular Motion Rotational Inertia Torque Center of Mass and Center of Gravity Centripetal/Centrifugal Force Angular Momentum Conservation of Angular Momentum Next time Skip pgs

Circular Motion Something undergoing circular motion can be moving around an internal axis (rotation) or and external axis (revolution) Rotational speed = # or revolutions (or rotations) time Usually revolutions per sec or min RPM = revs per min Tangential speed (or linear speed): the straight-line speed and object has in the direction tangent to the circle that it’s moving in. Rotation Revolution  The red spot is moving in a circle, but at any instant, it has a velocity in a straight-line direction tangent to the circle. If it were suddenly “released” from the circular motion, the spot would fly off in the tangent direction.

Tangential Speed Tangential speed depends on the radial distance from the axis of rotation. It also depends on how fast the object is rotating (the rotational speed). Tangential speed = radial distance x rotational speed v = r  Greek letter “omega” means “rotatational speed” Radial distance Tangential speed A bug located twice as far out on the turntable moves twice as fast as the bug located at half the radial distance. r 2r 2v v See Physics Place Demos

Rotational Inertia An object with lots of inertia is hard to start in motion, and it’s hard to stop if it’s already moving An object with lots of ROTATIONAL inertia is hard to start rolling, and it’s hard to stop it from rolling if it’s already rolling. Little rotational inertia More rotational inertia Even more rotational inertia The more mass an object has further from its axis of rotation, the more rotational inertia it will have.

Rotational Inertia Rotational inertia depends on both mass and radius of a rotating object A hoop always has more rotational inertia per unit mass than a solid disc. So a hoop is more reluctant to start rolling. For that reason, a disc will always roll down an incline faster than a hoop.

Question 1 Which stick will rotate to the floor first? A. Stick A B. Stick B C. The same A B

Which stick will rotate to the floor first? –A. Stick A –B. Stick B –C. The same Question 1 Answer A B

Torque A mass hung from a stick exerts a greater “twist” if it’s hung further from the pivot point. Hold on to stick here (pivot point) Smaller twist Greater twist The mass is the same. The twisting effect is called “torque”. The distance from the “pivot point” is called the “lever arm”. The amount of torque depends on the lever arm and the amount of force applied. Torque = Lever arm x Force

Torque For equilibrium to exists, torques must add to zero. The torques applied by the 2 kids are equal and opposite, so the see-saw doesn’t move. The lever arm is the distance of closest approach of the force. Notice that the torque applied by the smaller kid is the same whether she’s sitting on the seesaw or dangling beneath it, because the lever arm is still 3m. The torque can be increased by applying the force at right angles to the lever arm or by extending the lever arm. See Physics Place Demos