The average car today has a mass of 1100 kg, and when accelerating from rest, covers 0.25 miles in 15 seconds. Each rim and tire together has a diameter of 46 cm and a mass of 9.1kg. If we agree the rim and tire have the shape of a solid disk that rotates through its geometric center, what would be the kinetic energy of one of the tires, in Joules, at the end of the run?
I know KE=Iw^2
I calculated the moment of inertia to be 1.0465 kg*m
to find w, i calculated the number of revolutions for the given distance to be 278. dividing by time = 18.5rev/sec
converting to rad 116 rad/sec
so Ke= 116^2*1.0465 = 14081.704 j
am i right? i also need help with sig figs
actually
Ke = (1/2) I w^2
oops. but would the answer be correct if everthing was factored in?
Yes, you are correct in your calculation of the kinetic energy of one of the tires. Given that the moment of inertia (I) is 1.0465 kg*m and the angular velocity (w) is 116 rad/sec, you can use the formula KE = 1/2 * I * w^2 to calculate the kinetic energy.
Using this formula, KE = 1/2 * 1.0465 kg*m * (116 rad/sec)^2 = 14081.704 J.
As for significant figures, the general rule is to report your final answer with the same number of significant figures as the least precise value used in the calculation. In this case, it seems like all the values used in the calculation have either four or five significant figures, so it would be appropriate to report the final answer with four or five significant figures as well. Therefore, your answer of 14081.704 J with six significant figures can be rounded to 14080 J with four significant figures.