A cue ball (a uniform solid sphere of mass mm and radius R is at rest on a level pool table. Using a pool cue, you give the ball a sharp, horizontal hit of magnitude F at a height hh above the center of the ball. The force of the hit is much greater than the friction force ff that the table surface exerts on the ball. The hit lasts for a short time Δt. (a) For what value of hh will the ball roll without slipping? Use the impulse-momentum theorem to find the speed of the ball's center of mass immediately after the hit. Find the impulsive torque around the ball's center of mass exerted by the cue.
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 cue ball (a uniform solid sphere of mass mm and radius R is at rest on a level pool table. Using a pool cue, you give the ball a sharp, horizontal hit of magnitude F at a height hh above the center of the ball. The force of the hit is much greater than the friction force ff that the table surface exerts on the ball. The hit lasts for a short time Δt. (a) For what value of hh will the ball roll without slipping? Use the impulse-momentum theorem to find the speed of the ball's center of mass immediately after the hit. Find the impulsive torque around the ball's center of mass exerted by the cue.
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