A ball of mass 5.5 kg is released from rest from the top of a 4.0 m long hill that is inclined at 30°, as shown in figure. The ball rolls along the hill without slipping. The rotational inertia of a sphere of mass M and radius R about its center of mass is MR2. (cos 30° = 0.866, sin 30° = 0.5, g = 9.8m/s2) %3D a) Calculate the force due to friction acting on the ball as it rolls along the hill, b) Calculate the linear speed of the center of mass of the ball when it reaches the bottom edge of the hill, c) A wagon containing a box is at rest on the ground below the hill so that the ball falls the vertical distance of 3.0 m and lands and sticks in the center of the box. The total mass of the wagon and the box is 12 kg. Calculate the horizontal speed of the wagon immediately after the ball lands in it.
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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