An athlete whirls a 7.00-kg hammer 1.8 m from the axis rotation in a horizontal circle. Click to see picture.?

Question

An athlete whirls a 7.00-kg hammer 1.8 m from the axis rotation in a horizontal circle. Click picture link below to see the picture. If the hammer makes one resolution in 1.0 s, what is the centripetal acceleration of the hammer? What is the tension in the chain?

*picture link:
http://img88.imageshack.us/my.php?image=scan0003th2.jpg

Please help me with this problem.
I'm having trouble.

Answer 1

The speed (v) of the hammer is

v = w*r

where w is the angular speed and r is the radius of the circular orbit. The angular speed can be expressed

w = 2*pi/P

where P is the period, that is, the time it takes to make one revolution. This make the speed

v = 2*pi*r/P


You will notice that this is the circumference of the orbit divided by the time it takes to makes one revolution. The centripetal acceleration (ac) associated with circular motion is

ac = v^2/r

or

ac = r*(2*pi/P)^2

The tension on the chain balances the centrifugal force.

T =Fc = m*ac = m*r*(2*pi/P)^2

where m is the mass of the hammer.