A pirouette is a ballet move where the ballerina spins on her toes. The ballerina is able to control the angular speed of her spin by adjusting the position of her arms and legs; hence changing her mass distribution. A ballerina, with her arms and leg outstretched, is initially spinning with an angular speed of 6π rads/s. She then brings in her arms and legs, and her angular speed increases to 10π rads/s. (a) By modelling the ballerina with her arms and legs tucked in as a uniform cylinder of mass 60kg and radius 13cm, find her angular momentum after she has tucked her arms in. The moment of inertia of a uniform cylinder of mass M and radius R is given by I = 1/2 MR^2 (b) Hence, estimate her moment of inertia with respect to her axis of rotation when her arms and legs were outstretched
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 pirouette is a ballet move where the ballerina spins on her toes. The ballerina is
able to control the angular speed of her spin by adjusting the position of her arms
and legs; hence changing her mass distribution.
A ballerina, with her arms and leg outstretched, is initially spinning with an angular
speed of 6π rads/s. She then brings in her arms and legs, and her angular speed
increases to 10π rads/s.
(a) By modelling the ballerina with her arms and legs tucked in as a uniform
cylinder of mass 60kg and radius 13cm, find her
has tucked her arms in. The moment of inertia of a uniform cylinder of mass
M and radius R is given by I = 1/2 MR^2
(b) Hence, estimate her moment of inertia with respect to her axis of rotation
when her arms and legs were outstretched.
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