Suppose an object is rotating. It has an angular momentum defined as the product

Question

Suppose an object is rotating. It has an angular momentum defined as the product of the moment of inertia times the angular velocity. As long as no net external torque acts on the object, its angular momentum will stay the same. But what if the moment of inertia changes? In order to keep the same angular momentum, the angular velocity will adjust.
Suppose a figure skater is spinning with an initial angular speed of 5.30 rad/s. She then pulls her arms in, reducing her moment of inertia from a value of 2.12 kg·m/s to a value of 1.02 kg·m/s. What is her angular speed after pulling in her arms?

Suppose a figure skater is spinning with an initial angular speed of 4.60 rad/s. He then pulls his arms in, reducing his moment of inertia to 0.380 times its original value. What is his angular speed after pulling in his arms?

Explanation / Answer

a)

let,

initial angular speed w1=5.3 rad/sec

inital moment of inertia I1=2.12 kg*m^2

final angular speed is w2,

final moment of inertia I2=1.02 kg.m^2

here,

angular mometum is conseved

I1*W1=I2*W2

(2.12*5.3)=(1.02*W2)

===> final angular speed w2=11.01 rad/sec

b)

let,

initial angular speed w1=4.6 rad/sec

final angular speed is w2,

and

moment of Inertia I2=0.38*I1

agian,

I1*W1=I2*W2

(I1*4.6)=(0.38*I1*W2)

(4.6)=(0.38*W2)

===> final angular speed w2=12.1 rad/sec

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