Rotational energy, disk inertia, angular velocity, rotational kinematics, physics mechanics
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This document discusses the rotational energy of a disk, focusing on its inertia and angular velocity.
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[...] However, here the disk does not slide, so only the rotational energy remains. where I is the inertia of the disk and its angular velocity. One knows the inertia: And we know the relation between the angle and x : - If we consider a point on the outer edge of the disk which at any instant makes an angle with respect to the x-axis - As the generalized coordinate x measures the distance traveled by this point along the inclined plane - So , what amounts to saying - So 4. [...]
[...] Mechanics - Rolling on an inclined plane A disc on an inclined plane 1. At any instant, the height of the disc's center is given by: As x grows as the height decreases, then it descends: So the potential energy of the disk is; 2. The element Izz the inertia tensor is calculated by integration: [...]
