Angular Momentum of a Rigid Object Conservation of
-Angular Momentum of a Rigid Object -Conservation of Angular Momentum AP Physics C Mrs. Coyle
Angular Momentum of a Particle on Rotating Rigid Object • For a particle of mass mi of the object as shown. • L i = ri m i v i = m i ri 2 w • L and w vectors are perpendicular to the xy plane.
Angular Momentum of a Rotating Rigid Object • The angular momentum of the entire object, is the sum of the angular momentum vectors of all the individual particles
Rotational Form of Newton’s Second Law
Note: • The rotational form of Newton’s Second Law is also valid for a rigid object rotating about a moving axis provided the moving axis: (1) passes through the center of mass (2) is an axis of symmetry
Angular Momentum of a Bowling Ball • I=2/5 MR 2 • Lz = I w • The direction of the angular momentum is in the positive z direction
Conservation of Angular Momentum In the absence of a net external torque (the system is isolated) the net angular momentum of a system is conserved. Li = Lf I i wi = I f wf
Remember: • Closed System: A system that has no gain nor loss of mass. • Isolated System: A closed system with no net external force acting on it.
• Why does the skater spin faster when she pulls together arms? I i wi = I f wf
Video Link: Gyroscope • http: //www. youtube. com/watch? v=cquv. A_Ip Es. A&NR=1 • Bicycle Wheel Gyroscope (M. I. T. Physics) • http: //www. youtube. com/watch? v=8 H 98 Bg. Rz p. OM&NR=1
Gyroscope
Ex: Conservation of Angular Momentum
Video Link: Conservation of Angular Momentum (Bicycle Wheel) • http: //www. youtube. com/watch? v=UZl. W 1 a 6 3 KZs&NR=1
Note: For an isolated system: Energy, Linear Momentum, and Angular Momentum are conserved.
What happens to the angular speed of the system as the person moves towards the center of the Merry-Go. Round? Σ I i wi = Σ I f wf
Why does the kinetic energy of the system increase when the person moves towards the center?
Motion of a Top Precessional Motion : the motion of the axis of symmetry.
Angular Momentum of a Molecule
Ex: #30 • A student sits on a freely rotating stool holding two 3 kg masses. When his arms are extended horizontally, the masses are 1 m from the axis of rotation and he rotates with an angular speed of 0. 750 rad/s. The moment of inertia of the student plus stool is 3 kg m 2 and is assumed constant. The student pulls the weights inward horizontally to a position 0. 3 m from the rotation axis. a) Find the new angular speed of the student, b) The kinetic energy of the rotating system before and after he pulls the weights inwards. Ans: a) 1. 91 rad/s, b)2. 53 J , 6. 44 J
- Slides: 19