Rotational Kinetic Energy

A rotating object has kinetic energy due to its rotation:

• KErot = ½Iω²

For an object both translating and rotating (like a rolling ball):

• KEtotal = ½mv² + ½Iω²

Angular Momentum

Angular momentum (L) is the rotational equivalent of linear momentum:

• L = Iω
• For a point particle: L = r × p = mvr sin θ

Conservation of Angular Momentum

In the absence of external torques, angular momentum is conserved:

• Linitial = Lfinal
• I₁ω₁ = I₂ω₂

This explains why ice skaters spin faster when they pull their arms in (decreasing I increases ω).

Variables:

• m=mass
• v=velocity
• t=time
• KE=kinetic energy
• θ=angle (angular position)