A block of mass m sliding on a frictionless table is attached to a string that passes through a narrow hole through the center of the table. The block is sliding with speed v0 in a circle of radius r0. (Use any variable or symbol stated above as necessary.) (a) Find the angular momentum of the block.(b) Find the kinetic energy of the block.(c) Find the tension in the string.(d) A student under the table now slowly pulls the string downward. How much work is required to reduce the radius of the circle from r0 to r0/2?
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.
A block of mass m sliding on a frictionless table is attached to a string that passes through a narrow hole through the center of the table. The block is sliding with speed v0 in a circle of radius r0. (Use any variable or symbol stated above as necessary.)
(b) Find the kinetic energy of the block.
(c) Find the tension in the string.
(d) A student under the table now slowly pulls the string downward. How much work is required to reduce the radius of the circle from r0 to r0/2?
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