A ball weighing m = 200 g, suspended on a thread l = 60 cm long, describes a circle in the horizontal plane

A ball weighing m = 200 g, suspended on a thread l = 60 cm long, describes a circle in the horizontal plane. What is the kinetic energy Ek of the ball if it rotates with an angular velocity V = 10 rad / s?

m = 200 g = 0.2 kg.
l = 60 cm = 0.6 m.
w = 10 rad / s.
Ek -?
The kinetic energy of the ball Ek is determined by the formula: Ek = m * V ^ 2/2. Where m is the mass of the ball, V is the linear velocity of the ball.
The linear velocity V is determined by the formula: V = l * w, where l is the radius of the circle that the ball describes, in our case it is the length of the thread, w is the angular velocity of the ball.
Ek = m * (l * w) ^ 2/2.
Ek = 0.2 kg * (0.6 m * 10 rad / s)) ^ 2/2 = 3.6 J.
Answer: the ball has kinetic energy Ek = 3.6 J.



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