Rotational Momentum Observation Experiment 1 - Figure Skater - PowerPoint PPT Presentation

Rotational Momentum Observation Experiment 1 - Figure Skater Observation Experiment 2 - Diver

Rotational Momentum Observation Experiment 3 You sit on a chair that can spin with little friction and hold barbells far from your body. You spin yourself slowing then pull the barbells close to your body. Record your observations.

Rotational Momentum p = m v L = I ω

Impulse

Conservation of Angular Momentum The total angular momentum of a rotating body remains constant if the net external torque acting on it is zero.

Figure Skater A figure skater during her finale can increase her rotation rate from an initial rate of 1.0rev every 2.0s to a final rate of 3.0rev/s. If her initial moment of inertial was 4.6kg∙m 2 , what is her final moment of inertia? How does she physically accomplish this change?

Example 10-13 – Clutch Design M A =6.0kg, M B =9.0kg, R 0 =0.6m M A is accelerated from rest to ω 1 =7.2rad/s in Δt=2.0s. (a) Find angular momentum of M A . (b) Find torque required to get to ω 1 . M B is initially at rest but free to rotate without friction. M B falls vertically so it is firmly in contact with M A . The two rotate together and angular velocity is considerably reduced from ω 1 to ω 2 . (c) Why does this happen, and what is ω 2 ?

Ex10-15 Running on Circular Platform 60kg person at edge of 6.0m- diameter circular platform with I = 1800kg∙m 2 . The platform is initially at rest. When the person begins running at a speed of 4.2m/s (with respect to the ground) around the edge, the platform begins to rotate in the opposite direction. Calculate the angular velocity of the platform.

Vector Cross Product

Torque Vector

Angular Momentum of a Particle

Ex 12-20 Knight Two equal masses are at the ends of a massless 50 cm long rod. The rod spins at 2 rev/s at its midpoint. Suddenly, a compressed gas expands the rod out to a length of 160 cm. What is the angular velocity after the expansion?

Ex 11-7 Giancoli A bullet of mass m moving with velocity v strikes and becomes embedded at the edge of a cylinder of mass M with radius R o . The cylinder, initially at rest, begins to rotate about its symmetry axis, which remains fixed in position. Assuming no frictional torque, what is the angular velocity of the cylinder after the collision? Is kinetic energy conserved?

Ex 12-22 Knight A 2.0 kg block hangs from the end of a 1.5 kg, 1.0 m rod, together forming a pendulum that swings from a frictionless pivot at the top of the rod. A 10 g bullet is fired horizontally into the block, where it sticks, causing the pendulum to swing out to a 30 0 angle. What is the initial speed of the bullet?

Solution