You are given two spheres of the same mass and radius. In one sphere the mass is

Question

You are given two spheres of the same mass and radius. In one sphere the mass is uniformly distributed throughout its volume whilst the other is hollow with the mass all lying in a shell at the surface. You give each of them a spin on a surface so that their initial angular velocity is the same. Because of the small torque due to friction at the surface they will both begin to slow down. Which one spins the longest? Explain why. An old way of telling which egg is hard boiled and which is raw is to spin them on a surface. Again, one of them spins the longest. Which one and why? Historical Problem At some point in this part of the course I will use a gyroscope to illustrate aspects of rotational motion. Who invented the 'modem' gyroscope? When did he publish his invention? Who coined the name gyroscope? When? What does the word actually mean? What are inner and outer gimbals? Why is the inertial navigation system of a satellite based on a gyroscope?

Explanation / Answer

Problem R1:

Since,

For hollow sphere, Moment of inertia,

Ihs =2*M*R3/3

For solid sphere, moment of inertia,

Iss =2*M*R3/5

Tortque,

T = I*

Ratio of deceleration(angular)

ss/hs =(T/ Iss)/(T/Ihs) =Ihs/Iss =

ss/hs=(2*M*R3/3)/(2*M*R3/5)=5/3

ss>hs

Solid cylinder will 1st to stop. Hollow cylinder will spin the longest.

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