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Delve into the world of vertical and circular motion with hair-raising roller coaster speed and twirling objects on strings. Feel the excitement of non-uniform circular paths and the physics behind sustained vertical spinning. Understand gravitational forces and centripetal acceleration while exploring the physics of connected bodies in motion. Experience weightlessness in artificial gravity scenarios and satellites in circular orbits. Get ready for a journey through gravity-defying physics concepts!
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T maR x maR maR T T cannot be negative, the bob will fall down! T = 0; vcr mg mg mg mg Twirling a Ball on a String Vertically
Non-uniform Circular Motion If an object is moving in a circular path but at varying speeds, it must have a tangential component to its acceleration as well as the radial one.
Sustained vertical spinning • Ever wonder what a bike tire feels like? • At constant speed, the centripetal acceleration is constant (v2/r), but the direction of gravity keeps changing! • Feel heavier at bottom than at top • This ride definitely turns your world around!
water NB,W Bucket of Water a WE,W
Bridges & Speed Bumps The curvature of the bridge/bump and your speed determines if you are going to stay on the bump (N>0) or if you are going to bump: fly off it!
m M Connected Bodies Two different masses (m < M) are connected by a string going through a tube. Predict what will happen when you whirl the lighter mass with constant but high speed. Base your prediction on the CM model. • Mass M will be falling down since it is heavier • Mass M will be moving up and then stop • Mass M will move up and then will fall down • It is impossible to whirl the lighter mass around
m y T x mg M Connected Bodies - Analysis q If the mv2/R is > Mg, the mass M will accelerate upwards. Notice, the mass m will always rotate so the string is not horizontal. It happens so T has a vertical component to cancel out the mg!