If L is angular momentum of rotating body and E is its rotational kinetic energy then......
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Rotational kinetic energy can be expressed as: Erotational=12Iω2 E rotational = 1 2 I ω 2 where ω is the angular velocity and I is the moment of inertia around the axis of rotation. ... There is a close relationship between the result for rotational energy and the energy held by linear (or translational) motion.
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Concept:
- Rotational motion
- Angular momentum
- The rotating equivalent of linear momentum is angular momentum
- The moment of inertia
- The moment of inertia is a unit of measurement for the resistance a body exhibits to having the speed of its rotation about an axis changed by the application of torque.
Given:
- The angular momentum = L
- The rotational kinetic energy = E
Find:
- The rotational kinetic energy in terms of angular momentum
Solution:
L = mvr = mwr^2 (w = angular velocity)
E = 1/2 I w^2 (I = moment of inertia)
I = L/w
E = 1/2 L/w (w)^2
E = 1/2 Lw
The rotational kinetic energy is directly proportional to the angular momentum.
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