A child with a mass of 50 kg is on a circular frictionless platform with a mass of 100 kg. Treat the platform as a solid cylinder. The platform is initially rotating at a rate of 5 rmp (0.52 rad/s). The inner radius of the platform (where the child starts) is 2.0 m. The outer radius is 4.0 m. a. Determine the initial angular momentum of the system in kgm2 /s. b. If the child moves from the inner to the outer radius, determine the new angular velocity of the system. c. While at the outside radius, the child catches a 2.0 kg ball travelling at 10 m/s perpendicular to the radius. Determine the final angular momentum of the system.
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 child with a mass of 50 kg is on a circular frictionless platform with a mass of 100 kg. Treat the platform as a solid cylinder. The platform is initially
rotating at a rate of 5 rmp (0.52 rad/s). The inner radius of the platform (where the child starts) is 2.0 m. The outer radius is 4.0 m.
a. Determine the initial
/s.
b. If the child moves from the inner to the outer radius, determine the new
c. While at the outside radius, the child catches a 2.0 kg ball travelling at 10 m/s perpendicular to the radius. Determine the final angular
momentum of the system.
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