4. A race is set up with four different round objects rolling down a ramp (2 meters high). The four objects all have the same mass (10 kg) and radius (10 cm). The shapes are: (1) A solid sphere, (2) a solid cylinder, (3) a cylindrical hoop, and (4) a massless ring with four masses (each 2.5 kg) spaced evenly around the hoop. Assume no friction. a. Look up in your book what the moments of inertia are for the first three shapes. What is the moment of inertia for the shape #4? b. What is the mechanical energy of the objects at the top of the ramp? c. What is the mechanical energy of the objects at the bottom of the ramp? d. The mech. energy at the bottom is kinetic energy. What types of kinetic energy? e. Write an equation for the first object that sets the initial mechanical energy equal to the final kinetic energy. f. Think carefully, how is the angular velocity of the objects related to their velocities? g. Use part f to substitute for angular velocity in the conservation of energy equation. h. Solve for the final velocity of each object. 1. Whichwhieft basbestherettem Bothanamwith the Withentvalgrity? Theyasthe lowest?
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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