The rigid object shown in the figure consists of three balls and three connectin

Question

The rigid object shown in the figure consists of three balls and three connecting rods, with M = 1.0 kg, L = 0.20 m, and ? = 60?. The balls may be treated as particles, and the connecting rods have negligible mass. Determine the rotational kinetic energy of the object if it has an angular speed of 0.60 rad/s about (a) an axis that passes through point P and is perpendicular to the plane of the figure and (b) an axis that passes through point P, is perpendicular to the rod of length 2L, and lies in the plane of the figure.

Explanation / Answer

Here ,

for mass , M = 1 kg

L = 0.20 m

theta = 60 degree

angular speed , w = 0.60 rad/s

a) about the point P

moment of inertia , I = M * (2L)^2 + 2 * 2M * (L)^2

I = 8 * M * R^2

I = 8 * 1 * 0.20^2

I = 0.32 Kg.m^2

rotational kinetic energy = 0.5 * I * w^2

rotational kinetic energy = 0.5 * 0.32 * 0.6^2

rotational kinetic energy = 0.0576 J

the rotational kinetic energy is 0.0576 J

b)

for moment of inertia

moment of inertia , I = M * (2L)^2 + 2 * 2M * (L*cos(30))^2

I = 7 * M * R^2

I = 7 * 1 * 0.20^2

I = 0.28 Kg.m^2

rotational kinetic energy = 0.5 * I * w^2

rotational kinetic energy = 0.5 * 0.28 * 0.6^2

rotational kinetic energy = 0.0504 J

the rotational kinetic energy is 0.0504 J

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