Unit 11: Angular Momentum
A skater pulling her arms in, a gyroscope that precesses instead of falling — angular momentum conserved and torqued.
5 topics · 17 questions
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Angular Momentum of a Particle
- How it worksHow does angular momentum combine an object's position, mass, and velocity into one conserved quantity?
- Worked exampleFind the angular momentum of a 2 kg particle moving at 3 m/s at a perpendicular distance of 4 m from the axis.
- Common mistakeWhy isn't angular momentum the same thing as ordinary linear momentum, just measured a different way?
Your turn1 of 2
A 3.63 kg particle moves at 7 m/s at a perpendicular distance of 6 m from an axis. What is its angular momentum about that axis, in kg m2/s?Torque and the Rate of Change of Angular Momentum
- How it worksHow does net torque equal the rate of change of angular momentum, the rotational twin of F = dp/dt?
- Worked exampleFind the angular impulse delivered by a torque of 3 N m applied for 2 seconds.
- Common mistakeWhy doesn't an object need a torque acting on it just to keep spinning at a constant rate?
Your turn1 of 2
A torque of 6 N m is applied for 4 s. What is the resulting angular impulse (the change in angular momentum), in kg m2/s?Conservation of Angular Momentum
- How it worksHow does pulling mass closer to the rotation axis force angular velocity to increase to keep angular momentum fixed?
- Worked exampleFind the new angular velocity of a skater who reduces her moment of inertia from 5 to 2 kg m2 while spinning at 3 rad/s.
- Common mistakeWhy doesn't a skater visibly speeding up while pulling her arms in violate any conservation law?
- Going furtherWhat happens to a collapsing star's spin rate as it shrinks down into a tiny, dense neutron star?
Your turn1 of 2
A skater spinning at 5 rad/s with moment of inertia 7 kg m2 pulls her arms in, reducing her moment of inertia to 3 kg m2. What is her new angular velocity, in radians per second?Angular Momentum of Rigid Bodies and Systems
- How it worksHow does the total angular momentum of a system of particles add up from each particle's individual contribution?
- Worked exampleFind the total angular momentum of a 4 kg m2 disk spinning at 6 rad/s.
- Ties togetherHow does angular momentum conservation for a diver connect to the same law governing a collapsing gas cloud forming a star?
Your turn1 of 2
A disk with moment of inertia 6 kg m2 spins at 11 rad/s. What is its total angular momentum, in kg m2/s?Gyroscopic Precession
- How it worksHow does a torque perpendicular to a spinning object's angular momentum rotate that angular momentum's direction instead of its size?
- Worked exampleFind the precession rate of a gyroscope with angular momentum 0.5 kg m2/s under a torque of 0.1 N m.
- Common mistakeWhy doesn't gravity's torque on a spinning gyroscope just tip it straight over the way it would a stationary one?
- Going furtherWhat happens to a gyroscope's precession rate as its own spin rate increases?
Your turn1 of 2
A gyroscope has angular momentum 1.45 kg m2/s and experiences a torque of 0.342 N m. What is its precession rate, in radians per second?