Question

A pizza dough is thrown into the air, spinning. Originally, it has radius 22cm, mass 1.3kg, and velocity 50rpm. Coming down, it's radius is 26cm. Find its velocity.

Answer 1

Mass of the pizza dough = M = 1.3 kg

Initial radius of the pizza dough = R₁ = 22 cm = 0.22 m

Initial moment of inertia of the pizza dough = I₁

I₁ = MR₁²/2

Initial angular velocity of the pizza dough = ₁ = 50 rpm

Converting the angular velocity to rad/s,

₁ = 5.236 rad/s

New radius of the pizza dough = R₂ = 26 cm = 0.26 m

New moment of inertia of the pizza dough = I₂

I₂ = MR₂²/2

New angular velocity of the pizza dough = ₂

By conservation of angular momentum,

I₁₁ = I₂₂

(MR₁²/2)₁ = (MR₂²/2)₂

₁R₁² = ₂R₂²

(5.236)(0.22)² = ₂(0.26)²

₂ = 3.75 rad/s

Converting to revolutions per minute,

₂ = 35.8 rpm

Angular velocity of the pizza dough when it's coming down = 35.8 rpm