Chapter 8, Problem 53P

a.

To determine

To Find: The reason behind rotating rate reduced.

Answer to Problem 53P

The value of $I_2$ increases so the value of ${\omega }_2$ decreases.

Hence, the rotating rate reduced.

Explanation of Solution

Given Information:

Rate of rotation, ${\omega }_1=1.30\text{rev/s}$

Rate of rotation, ${\omega }_2=0.80\text{rev/s}$

Concept used:

By the law of conservation of angular momentum

  $L=I_2{\omega }_2=I_1{\omega }_1$

Here,

  $L$ is the angular momentum,

  $I_1,I_2$ is the moment of inertia,

  ${\omega }_1,{\omega }_2$ is the angular velocities.

Calculation:

For the constant value of angular momentum, here value of $I_2$ increases as a result value of ${\omega }_2$ decrease.

So, the rotating rate was reduced.

Conclusion:

As

  $I_2$ increases so, ${\omega }_2$ decreases and rotating rate also reduce.

b.

To determine

To find: Change in moment of inertia.

Answer to Problem 53P

Moment of inertia changed by a factor

  $1.625$.

Explanation of Solution

Given Information:

Rate of rotation ${\omega }_1=1.30\text{rev/s}$

Rate of rotation ${\omega }_2=0.80\text{rev/s}$

Concept used:

By the law of conservation of angular momentum

  $L=I_2{\omega }_2=I_1{\omega }_1$

Here,

  $L$ is the angular momentum,

  $I_1,I_2$ is the moment of inertia,

  ${\omega }_1,{\omega }_2$ is the angular velocities.

Calculation:

As, $I_1{\omega }_1=I_2{\omega }_2$

So, $I_1(1.3)=I_2(0.8)$

Here, $I_2=1.625I_1$

Conclusion: Moment of inertia is changed by a factor $1.625$ .