Water is drawn from a well with a bucket tied to the end of a rope whose other end wraps around a spherical pulley with radius R and mass Mpulley. Initially the bucket is high up and stationary. The mass of the bucket and water is m. Suddenly the person lets go of the crank, and the bucket of water falls down a distance d in time ∆t with an acceleration a. The rope has a tension T. Just before the bottom, the pulley is spinning with angular velocity ωf. Your answers need to be in terms of the given symbols. a. Draw the free-body diagram for the bucket. b. Draw the free body diagram for the sphere. Don’t forget the force at the center of the sphere due to the axle. c. Write an F = ma equation for the bucket of water
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.
Water is drawn from a well with a bucket tied to the end of a rope whose other end wraps around a spherical pulley with radius R and mass Mpulley. Initially the bucket is high up and stationary. The mass of the bucket and water is m. Suddenly the person lets go of the crank, and the bucket of water falls down a distance d in time ∆t with an acceleration a. The rope has a tension T. Just before the bottom, the pulley is spinning with
a. Draw the free-body diagram for the bucket. b. Draw the free body diagram for the sphere. Don’t forget the force at the center of the sphere due to the axle. c. Write an F = ma equation for the bucket of water. Show your axis and acceleration vector on the diagram. d. Write a torque equation for the spherical pulley. It needs to involve α and Mpulley. e. Write an energy conservation equation for the whole system.
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