Topics: Mechanics - Angular Momentum, Rotational Motion, Centripetal vs Centrifugal Forces
Equipment: Angular momentum apparatus with handle
Setup: Use one hand to hold the base firmly in place, while spinning the balls with the other hand. When the balls have reached a suitable rotational velocity, use your now free hand to grasp the handle, and pull it slowly to best observe the effect.
As the balls get closer together, they revolve around each other faster and faster. The mass and center of mass remain the same- it is only the distance from the axis of rotation that changes. The equation for angular velocity is ω = v/r, which tells us that angular velocity and the radius are inversely proportional, as is clearly demonstrated.
The equation L = Iω gives us a relationship between angular momentum and the angular velocity and moment of inertia, both of which depend on the radius. Simplifying I as the moment of two point masses of equal mass and radius from the axis of rotation, I = m1r12 + m2r22 = 2mr2 and L = 2mr2 * v/r = 2mvr. From this it is clear that in this case, the angular momentum is proportional to the radius.
Location: Shelf B-h5
Keywords: Rotate, Spin, Pull, Forces, Angle, Inertia