A long, thin rod is cut into two pieces, one being twice as long as the other. T

Question

A long, thin rod is cut into two pieces, one being twice as long as the other. To the midpoint of piece A (the longerpiece), piece B is attached perpendicularly, in order to form the inverted “ T ” shown in thedrawing. The application of a net external torque causes this object to rotate about axis 1 with an angular acceleration of 4.6 rad/s2. When the same net external torque is used to cause the object to rotate about axis 2, what is the angular acceleration?

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Explanation / Answer

The moment of inertia (I1) about axis 1 is 1/3*M*L^2

where M is the mass of the smaller rod and L is its length

Now the moment of inertia about axis 2 is I2 1/12*2M*(2L)^2 = 2/3*M*L^2

Therefore I2 = 2*I1

Since torque = I*, if you apply the same torque to an object with twice the moment of inertia then the acceleration will be 1/2

So 2 = 1/2 = 4.6/2 = 2.3 rad/s^2

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