A 1050kg car has four 15kg wheels. When the car is moving, what fraction of the total kinetic energy of the car is due to the rotation of the wheels about their axles? Assume that the wheels have the same rotational inertia as uniform disks of the same mass and size. Also, why do you not need the radius of the wheels?
I will be happy to critique your thinking on this.
You do not need the radius, because you are dealing with fractions of energy. When you work out the KE, radius will be there, and the same radius term will be in the rotational energy part, and the radius terms divide out.
The equation I came up with to use was KE(rotational)/KE(total)=4(.5mr^2w^2)/(4(.5mr^2w^2)+(.5mr^2w^2)) and got an answer of 5.4%. My physics teacher gives us answers to problems in our book that are almost the same as our homework problems, but when I used this equation with the corresponding question, I did not get the right answer. Where am I going wrong?
I agree with your formula, except how you used it. The masses of the wheels are not the same as the mass of the car, and the portion of KE translational has to use the mass of the cars.
The formula for the moment of inertia is actually incorrect for you.
I = (1/2)mr^2
so
K = (1/2)((1/2)mr^2)(w^2)
To find the fraction of total kinetic energy due to the rotation of the wheels, we need to calculate the total kinetic energy of the car and then determine the portion contributed by the rotation of the wheels.
The total kinetic energy of the car consists of two parts: translational kinetic energy and rotational kinetic energy.
The translational kinetic energy of the car can be calculated using the equation:
KE_trans = (1/2) * m * v^2,
where m is the mass of the car, and v is the velocity of the car.
In this case, the mass of the car (m) is given as 1050 kg. However, the velocity of the car (v) is not provided in the question. Therefore, without the velocity, we cannot determine the value of translational kinetic energy.
Moving on to the rotational kinetic energy, we need to determine the rotational inertia of the wheels about their axles. The rotational inertia of a circular object like a wheel depends on its mass and radius. However, in this case, the radius of the wheels is not given.
Without the value of the radius of the wheels, we cannot calculate the rotational kinetic energy. Therefore, we cannot determine the fraction of total kinetic energy due to the rotation of the wheels.
To solve this problem, we would need either the velocity of the car or the radius of the wheels.