A 625 gram basketball with a radius of 11.0 cm is a uniform hollow sphere that rolls without slipping along a horizontal surface of a floor such that the translational speed of the center of mass is 5.00 m/s. (a) What is the moment of inertia of the basketball? (b) What is the angular speed about the center of mass of the basketball as it rolls along the floor? (c) The basketball then reaches an incline that makes an angle of 30.0 above the horizontal. If we ignore any energy losses due to dissipative forces, then to what maximum vertical height above the floor will the basketball reach? Include a diagram of the situation.
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 625 gram basketball with a radius of 11.0 cm is a uniform hollow sphere that rolls without slipping along a horizontal surface of a floor such that the translational speed of the center of mass is 5.00 m/s. (a) What is the moment of inertia of the basketball? (b) What is the angular speed about the center of mass of the basketball as it rolls along the floor? (c) The basketball then reaches an incline that makes an angle of 30.0 above the horizontal. If we ignore any energy losses due to dissipative forces, then to what maximum vertical height above the floor will the basketball reach? Include a diagram of the situation.
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