Scratchy is trapped at the bottom of a vertical shaft. Itchy is rolling a heavy, thin- walled cylindrical shell (I = MR2) of mass 50 kg and radius 0.50 m toward a 5.0 m long, 30° ramp that leads to the shaft. The angular velocity of the cylindrical shell is 10 rad/s when Itchy releases it at the base of the ramp. All inanimate objects in this "experiment" obey the laws of physics. Itchy 'n' Scratchy are cartoon characters and are subject to the laws of cartoon physics. a) Who gets squashed in the end? That is, will the cylindrical shell make it to the top of the shaft and fall on Scratchy or will it turn around and roll back on Itchy? Show all work used to arrive at your answer. b) Would your answer to part a. change if the "experiment" took place on the moon where g = 1.6 m/s2? Explain your reasoning. c) Would your answer to part a. change if Itchy rolled a different hoop with the same radius and initial angular velocity but a mass of 100 kg? Explain your reasoning. d) Would your answer to part a. change if Itchy rolled a solid cylinder (I = MR2) with the same mass, radius, and initial angular velocity as the hoop? Explain
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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