A 0.338 kg basketball with radius r= 18.8 cm is left at the top of an inclined plane that makes an angle of e = 30° with respect to the horizontal. The ball starts from rest and rolls without slipping a distance d = 3.84 m reaching an angular speed of o = 3.00 rad/s. What is the ball's moment of inertia? (q48) a) 02.83 kg m? b) 04.24 kg m2 c) 0 0.00796 kg m2 d) O14 kg m2
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.
When a ball traveled distance 'd' on the inclined plane, the height of the slope at that instant will be given as,
The total potential energy stored in the ball at this height can be given as,
The velocity of the ball is,
The total energy of the ball at the bottom is,
Here, I denotes the moment of inertial of the ball.
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