Where is the ball’s moment of inertia, and is the ball’s angular velocity, usually measured in radians per second. If, instead, we roll a ball down a slope, the kinetic energy is in two forms, linear kinetic energy but also rotational kinetic energy, which is given by The gravitational potential energy is converted to linear kinetic energy as the ball drops by the time the ball hits the bottom of its fall all of the PE has been converted to KE. Where is the mass of the ball and is its velocity (which is increasing all the time as it falls and speeds up). But, in the case of the ball dropping vertically, the kinetic energy is all in the form of linear kinetic energy, given by This is the same as when the ball drops vertically. When it starts rolling down the slope, this gravitational potential energy gets converted to kinetic energy. When a ball rolls down a slope, it starts off at the top of the slope with gravitational potential energy. But, what about if we roll the two balls down a slope? If we build a track to keep them going straight, will a tennis ball roll down a slope at the same rate as a cannon ball? The answer is no, and I will explain why. This fact, contrary to the teachings of Aristotle, was one of the key breakthroughs which Galileo made in our understanding of motion. With a tennis ball and a cannon ball, they clearly have very different masses (weights), but will fall to the ground at the same rate. Galileo supposedly showed this idea by dropping objects of different weights from the tower of Pisa (although he probably never did this, see our book Ten Physicists Who Transformed Our Understanding of Reality). This is despite their having very different masses (weights). We all know that, if you drop two balls, say a tennis ball and a cannon ball, they will hit the ground at the same time. It is an interesting question, because it illustrates some things which are not immediately obvious. The other week I was asked to explain how a cylinder (or ball) rolling down a slope differs from e.g.
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