Consider the objects labeled A, B, C, and D shown in the figure. A В C D Each object is composed of identical thin sticks of uniformly distributed mass 7.59 kg and length 0.365 m. What are the moments of inertia IA, IB, Ic, and Ip of the objects about a rotation axis perpendicular to the screen and passing through the black dot displayed on each object? IA = kg-m? IB = kg-m? Ic = kg-m? Ip = kg-m?
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
![### Overview of Objects and Moments of Inertia
Consider the objects labeled A, B, C, and D as shown in the diagram.
#### Descriptions of Objects:
- **Object A**: Composed of four thin sticks arranged in a star-like formation, with each stick extending from a central black dot.
- **Object B**: Composed of two thin sticks, placed perpendicular to each other, with the intersection at the black dot.
- **Object C**: Composed of two parallel thin sticks, very close to each other, with one of their ends touching the black dot.
- **Object D**: Composed of three thin sticks, arranged similar to an L shape with a horizontal stick at the end.
Each object is composed of identical thin sticks with a uniformly distributed mass of 7.59 kg and a length of 0.365 m.
#### Task:
Determine the moments of inertia \( I_A, I_B, I_C, \) and \( I_D \) of the objects about a rotation axis that is perpendicular to the screen and passes through the black dot on each object.
#### Components:
- **Input Fields**: There are fields to input the calculated moments of inertia for each object in the units of kg·m².
### Calculating Moments of Inertia
- **Moment of Inertia Formula**:
\[
I = \frac{1}{3} m L^2
\]
where \( m \) is the mass and \( L \) is the length of each stick.
- Use this formula to calculate the moment of inertia for complex shapes by considering the configuration and number of sticks for each object.
### Entering Results:
- Fill in each calculated moment of inertia for the objects A, B, C, and D in the appropriate fields.
This exercise helps in understanding the application of rotational dynamics, specifically the computation of moments of inertia for various composite objects.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbf238986-8ffc-4b99-b1ca-533b8fe8c6d3%2F6978588a-988f-4d41-8eed-44475496eca0%2F4wfkv1h_processed.jpeg&w=3840&q=75)
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