Race car teams will spend exorbitant money to gain even the slightest edge on th

Question

Race car teams will spend exorbitant money to gain even the slightest edge on their competition. At many oval race tracks, such teams even shift the location of the engine toward the inside of the turn in an effort to lower the moment of inertia of the race car with respect to an axis passing through the center of the curve. Such a car (known as a supermodified) is shown to the right. Notice the engine is placed between the left-side wheels. Obviously, this car is designed to turn only left. Suppose that the engine has a mass of 1030 kg and is shifted in location 50.3 cm toward the inside of the curve. Assume that the engine is relatively small in comparison to the radius of curvature of the track and that the radius of the track turn is R = 28.5 m. Calculate the absolute value of the percent change in the moment of inertia of the engine about the center of curvature of the track caused by the shift in location.

Explanation / Answer

Given

mass of the engine, m = 1030kg

radius of curve , r = 28.5 m

shift in engine , s = 0.503 m

change in moment of inertia , delta I = m( r^2 - ( r-s)^2)

Put values

delta I = 1030 * ( 28.5^2 - 27.997^2)

delta I = 29270.53kg.m^2

initial moment of inertia , Ii = m*r^2

Ii = 1030 * 28.5^2

Ii = 836617.5 kg.m^2

the percent change in the moment of inertia of the engine about the center of curvature of the track , % = delta I/Ii * 100

% = 29270.53 /836617.5 * 100

% = 3.5%

the percent change in the moment of inertia of the engine about the center of curvature of the track is 3.5 %

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