What is the relationship between angular momentum and rotational kinetic energy?

A rotating object also has kinetic energy. When an object is rotating about its center of mass, its rotational kinetic energy is K = ½Iω2. Rotational kinetic energy = ½ moment of inertia * (angular speed)2. When the angular velocity of a spinning wheel doubles, its kinetic energy increases by a factor of four.

What is the relationship between angular momentum and the rotational velocity?

Because angular momentum is the product of moment of inertia and angular velocity, if the angular momentum remains constant (is conserved), then the angular velocity (rotational speed) of the skater must increase.

Is rotational kinetic energy conserved when angular momentum is conserved?

Angular momentum is therefore conserved in the collision. Kinetic energy is not conserved, because the collision is inelastic. It is possible that momentum is not conserved either because the force at the nail may have a component in the direction of the disk’s initial velocity.

What gives rise to a change in angular momentum?

If there is a net force, the momentum changes according to the impulse equation, and if there is a net torque the angular momentum changes according to a corresponding rotational impulse equation. This leads to some interesting effects, in terms of the conservation of angular momentum.

How is angular momentum different from angular velocity?

You have to know the moment of inertia of the rotating object, since angular momentum is the moment of inertia, I, times the angular velocity. Angular velocity is how fast something rotates (spins) around an axis. Momentum is mass times velocity.

What is the difference between angular velocity and angular momentum?

Angular momentum is defined as: The property of any rotating object given by moment of inertia times angular velocity. It is the property of a rotating body given by the product of the moment of inertia and the angular velocity of the rotating object.

When angular momentum is conserved what else is conserved?

Angular momentum, like energy and linear momentum, is conserved. This universally applicable law is another sign of underlying unity in physical laws. Angular momentum is conserved when net external torque is zero, just as linear momentum is conserved when the net external force is zero.

Why does the angular velocity decrease with time?

Since the rotational inertia of the system increased, the angular velocity decreased, as expected from the law of conservation of angular momentum. In this example, we see that the final kinetic energy of the system has decreased, as energy is lost to the coupling of the flywheels.

How does rotational inertia affect angular momentum?

Angular momentum is proportional to the moment of inertia, which depends on not just the mass of a spinning object, but also on how that mass is distributed relative to the axis of rotation. When the arms are pulled in close to the body, the skater spins faster because of conservation of angular momentum.

Does angular momentum change with radius?

Yes, angular momentum of a rotating body changes with radius.