A hollow sphere of mass 2.6 kg and radius 2 cm starts to roll (without slipping) down an incline of height 0.5 m. At the bottom of the incline, the sphere makes a head-on and perfectly inelastic collision with a box of mass 5.4 kg and the two objects slide together accross the ground. The coefficient of kinetic friction between the objects and the ground is 0.4. Determine the following quantities (take g = 9.81 m/s^2); (a) Kinetic energy of the sphere at the bottom of the incline (before collision) (in joules) (b) The speed of the system of two objects right after the collision (m/s) Hint: during the collision, model the two objects as point-like particles (c) The distance that the system of two objects travels from the bottom of the incline until they stop (m) (Give your answers as numbers (without any units or percentage) with 3 significant figures Use dot () for decimal point)
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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