A barbell consists of two identical masses, each of mas m, at the end of a massl

Question

A barbell consists of two identical masses, each of mas m, at the end of a massless rod. We will treat the masses as point masses. The barbell is then rotated in a plane (in two dimensions ) about a point along the rod which is a distance L1 from one mass and L2 from the other. The barbell rotates at a constant angular velocity. Which of the following statements is correct?

a. The kinetic energy of the barbell is 0.5*m*(L12 + L22)*w2. The masses rotate at different linear speeds.

b. The kinetic energy of the barbell is 0.5*m*L2*w2, since the masses rotate at the same linear speed and L is the length of the barbell.

c. The kinetic energy of the barbell is 0.5*m*(L12 + L22)*w2. The masses rotate at the same linear speed, since they rotate together.

d. The kinetic energy of the barbell is 0.5*I*w2 , where I, the moment of inertia, is mL2. Here, L is the length of the rod.

Explanation / Answer

Option A is correct, the barbaad rotate with different linear speed because their location from the axis of rotation is different but their angular velocity is same.

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