A composite object is made up of a uniform rod with mass of 2 kg and length of 3

Question

A composite object is made up of a uniform rod with mass of 2 kg and length of 3 m, and a point mass of 2 kg which is placed at the right end of the rod. What is the moment of inetria of the composite object about an axis perpendicular to the rod that passes through the left end of the rod?

The rod is initially held horizontally pivoted at the end without the point mass (i.e. the end with point mass is free to rotate in a clockwise direction). We then allow the object to swing in a vertical plane. What is the maximum angular velocity of the object?

Explanation / Answer

moment of inertia of rod about left end , I1 = m L^2 / 3

I1 = 2 x 3^2 / 3 = 6 kg m^2

moment of inertia of mass = m d^2 = 2 x 3^2 = 18 kg m^2

moment of inertia of system, I = I1 + I2 = 24 kg m^2 .........Ans

Applying energy conservation,

PEi + KEi = Pef + KEf

m g L + m g L + 0 = ( 0 + m g L/2) + (I w^2 /2 )

1.5 m g L = I w^2 /2

1.5 x 2 x 9.8 x 3 = 24 w^2 /2

w = 2.71 rad/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.