A 0.5 kg mass is being swung over someones head in a circle of 0.5 meters in dia

Question

A 0.5 kg mass is being swung over someones head in a circle of 0.5 meters in diameter. If the weight is moving at a speed of 2 rev/sec, what is the speed of the mass in meters per second? What is the tension of the cable?

b. ) If the other end of the cable was attached to a weight through a contraption that doesn't provide any friction, how much weight is needed to keep the cable length from inceasing (a.k.a, such that the bottom weight is static equilibrium?) What is the rotational energy of the rotating masses (consider the masses on the end of the cable as a point mass)?

Explanation / Answer

a) angular speed, w = 2 rev/s = 2 x 2pi rad/s = 12.57 rad/s

linear speeed, v= w r = 12.57 x (0.5/2) = 3.14 m/s

T = mw^2 r = 0.5 x 12.57^2 x (0.5/2) = 19.75 N

b) for equilibrium,

Fnet = T - mg = 0

m x 9.8 = 19.75

m = 2.02 kg

rotational energy = I w^2 / 2 = ( m r^2) w^2 /2

       = (0.5 x (0.5/2)^2 ) 12.57^2 / 2

      = 2.47 J

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