Question

You attach a 100-g puck to a string and let the puck glide in a circle on a horizontal, frictionless air table. The other end of the string passes through a hole at the center of the table. You pull down on the string so that the puck moves along a circular path of radius 0.50 m. It completes one revolution in 6.0 s.

If you pull harder on the string so the radius of the circle slowly decreases to 0.40 m, what is the new period of revolution?

Tf =

Answer 1

Mass of the puck = M = 100 g = 0.1 kg

Initial radius of the circle = R₁ = 0.5 m

Initial moment of inertia of the system = I₁

I₁ = MR₁²

I₁ = (0.1)(0.5)²

I₁ = 2.5 x 10^-2 kg.m²

Initial time period of one revolution = T₁ = 6 sec

Initial angular velocity of the puck = ₁

₁ = 1.047 rad/s

New radius of the circle = R₂ = 0.4 m

New moment of inertia of the system = I₂

I₂ = MR₂²

I₂ = (0.1)(0.4)²

I₂ = 1.6 x 10^-2 kg.m²

New angular speed of the puck = ₂

By conservation of angular momentum,

I₁₁ = I₂₂

(2.5x10^-2)(1.047) = (1.6x10^-2)₂

₂ = 1.636 rad/s

New time period of one revolution = T₂

T₂ = 3.84 sec

New period of revolution = 3.84 sec