A solid metal disk with moment of inertia I, radius R, and mass m1 can rotate freely about a frictionless axis passing through its center. A light string is wrapped around the disk and connects to a hanging mass m2. The hanging mass is released from rest at a distance d above the ground and accelerates downward with acceleration awhile the disk rotates through an angle q. a) Find an expression for the angular accelerationaof the diskin terms of m2, I, R, and any necessary constants. b) Find an expression for the time it takes for the hanging mass to reach the ground. Write your answer in terms of q, a, and any necessary constants. c) Find an expression for the angular velocity of the disk just before the hanging mass hits the ground. Write your answer in terms of q, a, and any necessary constants.
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.
A solid metal disk with moment of inertia I, radius R, and mass m1 can rotate freely about a frictionless axis passing through its center. A light string is wrapped around the disk and connects to a hanging mass m2. The hanging mass is released from rest at a distance d above the ground and accelerates downward with acceleration awhile the disk rotates through an angle q.
a) Find an expression for the angular accelerationaof the diskin terms of m2, I, R, and any necessary constants.
b) Find an expression for the time it takes for the hanging mass to reach the ground. Write your answer in terms of q, a, and any necessary constants.
c) Find an expression for the
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