The top edge of a thin rectangular metal plate with a mass of 2.60 kg is attached to a horizontal rod parallel to the edge of the plate. The plate hangs from this rod and is free to rotate about it without friction. The vertical height of the plate is 45.0 cm. The plate is pulled to the right until it makes an angle of 28.0° from vertical and then released from rest. At the same time, a piece of clay is tossed at the plate, moving to the right. At the moment the plate reaches vertical, moving left, it collides with the clay. The piece of clay strikes the plate at its bottom edge, moving to the right perpendicular to the plate at the moment of impact. Its mass is 380 g and its speed just before impact is 160 cm/s. The clay sticks to the plate after impact. (a) What is the angular speed (in rad/s) of the plate the instant before it collides with the clay? (Round your answer to at least two decimal places.) rad/s (b) What is the angular speed (in rad/s) of the plate-clay system immediately after the collision? rad/s (c) What is the magnitude of the maximum angular displacement from the vertical (in degrees) that the plate-clay system will reach after the collision?
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.
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