Download Newton*s 2nd Law for Rotation, Angular Momentum

Newton’s 2nd Law for Rotation,
Angular Momentum, Rotational
Kinetic Energy
Rotation
Physics
Mr. McCallister
Newton’s 2nd Law for Rotation
• Recall Newton’s Second Law:
–F=ma
– Force = mass x acceleration
• Newton’s Second Law for Rotation states:
–τ=Iα
– torque = moment of inertia x angular acceleration
Practice 8C, #2-3
• #1
– Worked on board
• Due NEXT Tuesday, 2-16-10
Angular Momentum
• Recall linear (or translational) momentum:
–p=mv
– momentum = mass x velocity
• Angular momentum is “the product of a
rotating object’s moment of inertia and
angular speed about the same axis
– Symbol: L , Unit: kg m2 / s
–L=Iω
– angular momentum = moment of inertia x angular
speed
Conservation of Angular Momentum
• If no net torque is acting on a system, then the
system’s angular momentum will be
conserved
• Example: figure skater’s spin
– Decreasing I will yield increased ω to conserve L.
Practice 8D, #2-5
• #1
– Worked on board
• Due NEXT Tuesday 2-16-10
Rotational Kinetic Energy
• Recall linear (or translational) kinetic energy
– KEtrans = ½ m v2
• Rotational kinetic energy is due to an object’s
rotational motion
– KErot = ½ I ω2
– rotational kinetic energy = ½ x moment of inertia x
(angular speed)2
Conservation of Mechanical Energy
• If only conservative forces (i.e. gravitational,
normal) are acting on a system, the system
will conserve mechanical energy
• However, now ME = KEtrans + KErot + PEg
– ME = ½ m v2 + ½ I ω2 + m g h
Practice 8E #2,3 and Section Review
• Sample Problem 8E
– worked on board
• Due NEXT Tuesday, 2-16-2010