For a spinning object, on the other hand, the angular momentum must be considered as the summation of the quantity mvr for all the particles composing the object.

Rotational collisions conserve angular momentum When objects collide without a net external torque, the angular momentum is constant. The two objects exert equal, but opposite angular impulses upon each other to maintain the total angular momentum of the colliding system.

Angular momentum, like energy and linear momentum, is conserved.

So, spin is an angular momentum, just orbital angular momentum is. Spin is the angular momentum of a particle in the frame where the particle is at rest. If the particle is moving, then there are additional contributions to it’s angular momentum, namely the orbital angular momentum.

The kinetic energy in a uniform circular motion is constant. This is true because the speed in a uniform circular motion is constant and kinetic energy depends on the speed of the object as seen the equation of the kinetic energy.

Uniform circular motion is a motion in a circular path at constant speed. An object reaches escape speed when the sum of its kinetic energy and its gravitational potential energy is equal to zero.

So a change in momentum corresponds to a change in kinetic energy. This is the essence of Newton’s second law: Applying a force to a mass changes the momentum of that mass. An acceleration just represents this change in momentum for an object that has a constant mass.

Negative kinetic energy equals half the potential energy (−K = ½U). Potential energy equals twice the total energy (U = 2E). Twice the kinetic energy plus the potential energy equals zero (2K + U = 0).

Key Points

1. Rotational kinetic energy can be expressed as: Erotational=12Iω2 E rotational = 1 2 I ω 2 where ω is the angular velocity and I is the moment of inertia around the axis of rotation.
2. The mechanical work applied during rotation is the torque times the rotation angle: W=τθ W = τ θ .

We see from this equation that the kinetic energy of a rotating rigid body is directly proportional to the moment of inertia and the square of the angular velocity….Moment of Inertia.

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.