A Uniform Ball with Diameter of 10 Cm $2.2 \times 10 ^ { - 3 } \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$

question 145

Essay

A uniform ball with diameter of 10 cm rolls without slipping on a horizontal tabletop. The moment of inertia of the ball about an axis through its center is $2.2 \times 10 ^ { - 3 } \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ translational speed of its center is 0.45 m/s.
(a) What is its angular speed of the ball about its center of mass?
(b) What is the rotational kinetic energy of the ball?
(c) What is the ball's angular momentum about its center of mass?

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Definitions:

Pareto Efficient

A distribution of resources where improving the situation of one person cannot be achieved without detriment to another.

Net Benefit

The total positive effects or outcomes of a decision or action minus its total negative effects or costs.

Labor Supply Decisions

The choices individuals make regarding how much labor to supply to the market, influenced by factors such as wages, working conditions, and personal preferences.

Pareto Optimal

A distribution of resources where it's infeasible to enhance the well-being of one individual without adversely affecting another.