Question

An metal flywheel inside an engine increases its temperature by 40 ◦C. Assuming the flywheel to be a uniform circular disk, calculate the fractional change in the moment of inertia of the flywheel, which has a coefficient of linear expansion of 24 × 10−6/ K.

A) 4.80e-04
B) 2.88e-03
C) 4.80e-03
D) 1.92e-03
E) 3.36e-03

Answer 1

The fractional change in the moment of inertia of a heated metal flywheel is 1.92 x 10^−3, considering a temperature increase of 40 °C and a coefficient of linear expansion of 24 x 10^−6/K.

Step-by-step explanation:

When a metal flywheel heats up and its temperature increases by 40 °C, the flywheel will expand due to thermal expansion. Considering the coefficient of linear expansion is 24 × 10^−6/ K, the fractional change Δr/r in the radius of the flywheel can be calculated using the formula Δr/r = α ∗ ΔT, where α is the coefficient of linear expansion and ΔT is the temperature change.

Therefore, the fractional change in radius is 24 x 10^−6 x 40 = 9.6 x 10^−4. The moment of inertia I of a uniform circular disk is given by I = (1/2)mr2, where m is the mass and r is the radius of the disk. The fractional change in the moment of inertia ΔI/I equals 2Δr/r since the moment of inertia is proportional to the square of the radius.

Thus, ΔI/I = 2 x 9.6 x 10^−4 = 1.92 x 10−3, which corresponds to option D.