Question

what happens to the acceleration (of a ball going around in a circle tethered to a string) if:

1) radis of the circle halves and the period of rotation stays the same
2) the peiod of rotation halves and the radius stays the same
3) the period doubles and the speed doubles (the radius changes as necessary)

this is my reasoning:
1) v=2(pi)r divided by T, therefore, if radius is halved, then the velocity will be halved, and thus the acceleration would be halved.

2)velocity is twiced, therefore, the accerleration is quadrupled based on a=v^2/r

3)i'm not sure at all.

the answers are:
-quadruples, quarters, stays the same, halves, doubles.

any help is appreciated!

Answer 1

acceleration= 4PI^2 r/T

a) acceleration is halved, right?
2) if T is halved, then acceleration is doubled
3) If speed doubles, and period doubles, what happened to r?
v=2PI r/T
TV=2PI r so r quadrupled
a= v^2/r so a stays the same.