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Four balls slide down a cycloid curve from different positions, but they arrive at the bottom at the same time. The blue arrows show the points' acceleration along the curve. On the top is the time-position diagram. Objects representing tautochrone curve
A snowball being rolled down a hill, with a dangerous outcome. The common analogy is with the rolling of a snowball down a snow-covered hillside. As it rolls the ball will pick up more snow, gaining more mass and surface area, and picking up even more snow and momentum as it rolls along.
Torque-free precessions are non-trivial solution for the situation where the torque on the right hand side is zero. When I is not constant in the external reference frame (i.e. the body is moving and its inertia tensor is not constantly diagonal) then I cannot be pulled through the derivative operator acting on L .
The curve of fastest descent is not a straight or polygonal line (blue) but a cycloid (red).. In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) ' shortest time '), [1] or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead ...
The animation illustrates rolling motion of a wheel as a superposition of two motions: translation with respect to the surface, and rotation around its own axis.. Rolling is a type of motion that combines rotation (commonly, of an axially symmetric object) and translation of that object with respect to a surface (either one or the other moves), such that, if ideal conditions exist, the two are ...
Under a constant torque of magnitude τ, the speed of precession Ω P is inversely proportional to L, the magnitude of its angular momentum: = , where θ is the angle between the vectors Ω P and L. Thus, if the top's spin slows down (for example, due to friction), its angular momentum decreases and so the rate of precession increases.
A mountain biker riding a trail which follows the line of greatest slope, or fall line.. In mountain biking the line of greatest slope defines the fall line, which is the path a trail will follow to descend a hill or mountain with the shortest path, [1] and will also cause the rider to gain the most velocity (assuming brakes are not used, and other factors such as rolling resistance are equal).
The horizontal axis shows the rotational speed (in rpm) that the crankshaft is turning, and the vertical axis is the torque (in newton-metres) that the engine is capable of providing at that speed. Torque forms part of the basic specification of an engine: the power output of an engine is expressed as its torque multiplied by the angular speed ...