Aslender rod is 80.0 cm long and has mass 0.370 kg . a small 0.0200-kg sphere is welded to one end of the rod, and a small 0.0500-kg sphere is welded to the other end. the rod, pivoting about a stationary, frictionless axis at its center, is held horizontal and released from rest. what is the linear speed of the 0.0500 kg sphere as it passes through its lowest point?

1.10 m/s

Explanation:

Linear speed is given by

Kinetic energy is given by

Potential energy

PE= mgh

From the law of conservation of energy, KE=PE hence

where m is mass, I is moment of inertia, is angular velocity, g is acceleration due to gravity and h is height

Substituting m2-m1 for m and 0.5l for h, for we obtain

and making v the subject

For the rod, moment of inertia and for sphere hence substituting 0.5L for R then

For the sphere on the left hand side, moment of inertia I

while for the sphere on right hand side,

The total moment of inertia is therefore given by adding

Substituting for I in the equation

Then we obtain

This is the expression of linear speed. Substituting values given we get

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