A square plate with sides 1.9 m in length can rotate around an axle passing through its center of mass (CM) and perpendicular to its surface (see figure below). There are four forces acting on the plate at different points. The rotational inertia o the plate is 19 kg - m. Use the values given in the figure to answer the following questions. (Assume e 43°. Express your answers in vector form.) 30.0N N009 CM 20.0 N e400N (a) What is the net torque acting on the plate? N-m (b) What is the angular acceleration of the plate? rad/s
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.
![**Problem Statement:**
A square plate with sides 1.9 m in length can rotate around an axle passing through its center of mass (CM) and perpendicular to its surface (see figure below). There are four forces acting on the plate at different points. The rotational inertia of the plate is 19 kg·m². Use the values given in the figure to answer the following questions. (Assume θ = 43°. Express your answers in vector form.)
**Diagram Explanation:**
- The square plate is shown with its center of mass (CM) marked.
- Four forces are applied at different points on the plate:
- A 30.0 N force directed upwards along the y-axis.
- A 60.0 N force directed downwards along the y-axis.
- A 20.0 N force directed leftwards along the x-axis at an angle θ = 43°.
- A 40.0 N force directed rightwards along the x-axis.
**Questions:**
(a) What is the net torque acting on the plate?
- τ = [ ] N·m
(b) What is the angular acceleration of the plate?
- α = [ ] rad/s²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c0a33fd-0568-4a66-9e09-cb4c2724e152%2F70314cca-472c-4cbc-95bf-0e0bae221235%2Fhuj278u_processed.jpeg&w=3840&q=75)
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