The axis of rotation of a thin plate is located at the left side, as shown in the figure. Calculate the moment of inertia I if the plate has a length L of 5.00 cm, a width w of 3.00 cm, and a uniform mass density of 2.50 g/cm².
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.
![**Moment of Inertia Calculation for a Thin Plate**
The axis of rotation of a thin plate is located at the left side, as shown in the figure.
**Task:**
Calculate the moment of inertia \( I \) if the plate has a length \( L \) of 5.00 cm, a width \( w \) of 3.00 cm, and a uniform mass density of 2.50 g/cm\(^2\).
**Diagram Description:**
The diagram features a rectangle on the right, representing the thin plate. The left side of the rectangle is aligned with a vertical dashed line, which indicates the axis of rotation. An arrow on the left side signifies rotation around this axis. The rectangle has marked dimensions: the vertical side is labeled \( w \) (width), while the horizontal side is labeled \( L \) (length).
**Formula Placeholder:**
\[ I = \underline{\hspace{40mm}} \, \text{kg}\cdot\text{m}^2 \]
This setup helps visualize the parameters involved in calculating the moment of inertia for the given plate dimensions and characteristics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a5c500a-af21-4189-b630-ff7bbb03bf84%2F8c737f78-87b7-440b-9a60-1e9f03abc00f%2F15c2j7n_processed.png&w=3840&q=75)
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