Start with a freely rotating hoop-like wheel of mass m = 30kg and radius 25cm, rotating at 125 rpm. 1. Sketch this wheel, write out equations for and calculate it’s L and rotational KE. The wheel hits the ground, bounces and skids while negative accelerating, eventually locking to the ground so that its linear velocity equals its rotational velocity times its radius. 2. Write this (roll no slip) equation. Sketch this final rolling wheel on the ground, include a vector for the linear velocity. 3. Write an equation conserving angular momentum before and after the drop. Solve your equation for final angular velocity (both algebra and a number). Briefly explain. 4. Solve for final rotational and linear kinetic energy and compare to initial rotational energy. How much energy was lost during the skidding process? (Formula and number).
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.
Start with a freely rotating hoop-like wheel of mass m = 30kg and radius 25cm, rotating at 125 rpm.
1. Sketch this wheel, write out equations for and calculate it’s L and rotational KE.
The wheel hits the ground, bounces and skids while negative accelerating, eventually locking to the ground so that its linear velocity equals its rotational velocity times its radius.
2. Write this (roll no slip) equation. Sketch this final rolling wheel on the ground, include a vector for the linear velocity.
3. Write an equation conserving
4. Solve for final rotational and linear kinetic energy and compare to initial rotational energy. How much energy was lost during the skidding process? (Formula and number).
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