A block of mass m is attached to a string that is wrapped aroundthe circumference of a wheel of radius R and moment of inertia I. The wheel rotates freely about its axis and the string wrapsaround its circumference without slipping. Initially the wheelrotates with an angular speed v, causing the block to rise with alinear speed v. To what height does the block rise before comingto rest? Give a symbolic answer.
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 block of mass m is attached to a string that is wrapped around
the circumference of a wheel of radius R and moment of inertia I. The wheel rotates freely about its axis and the string wraps
around its circumference without slipping. Initially the wheel
rotates with an angular speed v, causing the block to rise with a
linear speed v. To what height does the block rise before coming
to rest? Give a symbolic answer.
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