Vertical Circular Motion

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Presentation transcript:

Vertical Circular Motion

Roller Coaster

Roller Coaster

Twirling a Ball on a String Vertically x mg T T mg maR T = 0; vcr mg maR T cannot be negative, the bob will fall down! mg maR

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.

Ferris Wheel

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!

Bucket of Water NB,W 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!

How fast do you need to drive to leave the ground?

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. m M 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

Connected Bodies - Analysis q m M T mg x y 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!

Satellites in Circular Orbits

Weightlessness in Space Shuttle

Artifical Gravity