Physics question!?

Question

Assume: The length of the athlete's arm is included in the length given for the chain below.

An athlete whirls a 6.81 kg hammer tied to the end of a(n) 1.3 m chain in a horizontal circle. The hammer moves at a rate of 1.47 rev/s.

a) What is the centripetal accelaration of the hammer? (in m/s^2)

b) What is the tension in the chain? (in N)

Answer 1

The angular acceleration α can be found from

α = r ω^2

where α is the angular acceleration in radians / sec^2 and ω is the angular velocity in radians per second. You know the angular velocity; it's 1.47 rev / sec or ( 2π ) ( 1.47 ) radians / sec. Now you can compute the angular acceleration α.

We are nearly there. The linear acceleration a is

a = rα

Now you have the centripetal acceleration.

That centripetal acceleration is provided by tension in the cable. Newton's Second Law tells us that the tension must be equal to ma, so to find the tension, multiply the centripetal acceleration by the mass of the hammer.