A ball of mass 1.25 kg is attached by a 1.4 meter long massless rope to the top

Question

A ball of mass 1.25 kg is attached by a 1.4 meter long massless rope to the top of a vertical pole. The ball swings in a horizontal circle at a constant rate of ? rad/s with the rope making an angle of 29

A ball of mass 1.25 kg is attached by a 1.4 meter long massless rope to the top of a vertical pole. The ball swings in a horizontal circle at a constant rate of ? rad/s with the rope making an angle of 29 degree with the vertical. What is the rotational kinetic energy of the ball? (include units with answer)

Explanation / Answer

The sum of forces along y is

Tcos29 - mg = 0

Thus,

T = mg/cos29

T = 14.01 N

Thus, the sum of forces along x is the centripetal force,

m w^2 r = Tsin29

m w^2 r = 6.79 N

Multiplying both sides by r/2, we match the expression for KE = m w^2 r^2 /2,

KE = m w^2 r^2 / 2 = 6.79 N * (r/2)

As r = 1.4 m * sin 29 = 0.6787 m,

KE = 2.30 J   [ANSWER]

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