A diver leaves the platform with her body straight. Her body is in a relatively slow rotation, with an angular speed of 4.0 rad/s. She then tucks into a pike position, with her body essentially folded in half. We can use a simple model to understand what happens next. First, model her 50 kg, 1.8 m body as uniform. Next, assume that when she goes into a pike position, she really does fold her body exactly in half. In terms of this model, a. What is her initial moment of inertia?b. What is her moment of inertia in the pike position?c. What is her angular speed in the pike position?d. How many rotations does she complete in the 1.3 s that she holds the pike position?
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 diver leaves the platform with her body straight. Her body is in a relatively slow rotation, with an angular speed of 4.0 rad/s. She then tucks into a pike position, with her body essentially folded in half. We can use a simple model to understand what happens next. First, model her 50 kg, 1.8 m body as uniform. Next, assume that when she goes into a pike position, she really does fold her body exactly in half. In terms of this model,
a. What is her initial moment of inertia?
b. What is her moment of inertia in the pike position?
c. What is her angular speed in the pike position?
d. How many rotations does she complete in the 1.3 s that she holds the pike position?
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