A pulley attached to the top of a ramp has a rope wrapped around it (like a spoon of thread). Treat the pulley like a solid cylinder. The rope is attached to a solid sphere at its axle. The axle turns without friction. The system is released from rest. The rope unwinds from the pulley and the sphere rolls 8. without slipping down the hill. The mass of the pulley is 20.0kg and has a radius of 0.250m. The sphere has a mass of 50.0kg and a radius of 0.500m. The ramp makes an angle of 40.0° with the horizontal. (Solve this problem using Force-Torque Principles.) What is the acceleration of the sphere? а. b. What are the angular accelerations of the pulley and the sphere?
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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