What happens to circular motion when the radius changes?

[pharaoh]

what will happen in circular motion if the radius increase, and if it decrease.

what effects and causes that will make an abject successfuly complete its circular motion in increasing radius (like car toy loop)

for the first question my answer is if the radius increase the centrpetal acceleration will get smaller and if the radius decrease the centrpetal acceleration will get bigger. but i don't know what roll does the centrpetal acceleration have on circular motion.

 

[antonantal]

It's the centrifugal force (the reaction to the centripetal force) that enables the toy car to complete the loop. The centrifugal acceleration also increases when the radius of the circular motion decreases. So if the vectorial sum of the gravitational and the centrifugal acceleration doesn't point away from the "road" then the toy car will complete the loop.

 

[berkeman]

What are the equations for centripetal acceleration (in terms of omega or velocity)? What is the energy in uniform circular motion? What does an ice skater do in a spin to speed up the spin?

 

[pharaoh]

the formula that i know is centripetal acceleration (Ac)=v^2/r