# Fraction of Kinetic Energy from Rotating Wheels in Moving Car

• Ignitia
In summary, the question asks for the ratio of the rotational kinetic energy of the four wheels to the total kinetic energy of the car. The solution involves finding the kinetic energy of the car, which is 1/2 multiplied by its mass and velocity squared, and then finding the ratio using the rotational kinetic energy equation for a wheel. It is important to note that the total kinetic energy of the car is not the same as the rotational kinetic energy of the wheels.
Ignitia

## Homework Statement

A 1000-kg car has four 10-kg wheels. When the car is moving, what fraction of its total kinetic energy is due to rotation of the wheels about their axles? Assume that the wheels the same mass and size.

## Homework Equations

Rolling Wheel:
K=1/2 Icomω2 + 1/2mv2

Inertia for Wheel:
I=1/2mv2

v=ωr
ω=v/r

## The Attempt at a Solution

(Per wheel)
K=1/2 Icomω2 + 1/2mv2
K=1/2 [1/2mv2*vSUP]2[/SUP]/r2 + mv2]
K=1/2 [1/2mv2 + mv2]
K=1/2 [3/2mv2]
K=3/4 mv2]

The book states the answer to be 0.020
How?

What is the total kinetic energy of the car?

Also, are the wheels assumed to be rings or cylinders?

Orodruin
Orodruin said:
What is the total kinetic energy of the car?
It's not given. Although that'd be KE = 1/2mv^2, whatever the velocity is.

kuruman said:
Also, are the wheels assumed to be rings or cylinders?
Cylinders.

Well, you need the ratio of the kinetic energy of the four wheels about their center of mass to the kinetic energy of (the car's center of mass + the kinetic energy of the four wheels about their center of mass). Do you think you can find this ratio?

Ignitia said:
It's not given.
Of course not, but your problem asks you to find the ratio of the rotational energy of the wheels and the total kinetic energy. The car’s kinetic energy is clearly included in that so you better find it.

Well, car's is KE=1/2mv^2,
and [KE=3/4mv^2]x4 = 3mv^2

And that doesn't look right.

Of course it does not look right. Does the car have the same mass as a wheel?

Well, this shows I'm half asleep.

4*[3/4(10v^2)]/1/2*(960v^2) = 4*[3/4(10)]/1/2*(960) = 4*7.5/.5*960 = 1/16 = .06

It's still not correct though.

Note that you were just asked about the rotational kinetic energy of the wheels. Not the total kinetic energy of the wheels.

Late reply sorry. I got it now, thanks!

## What is "KE of more than one wheel"?

The "KE of more than one wheel" refers to the kinetic energy (KE) generated by a system that involves multiple rotating wheels. This can include vehicles such as cars and bicycles, as well as machinery with multiple rotating parts.

## How is the KE of more than one wheel calculated?

The KE of more than one wheel is calculated by adding together the individual KE of each wheel. This can be calculated using the equation KE = 1/2 * m * v^2, where m is the mass of the wheel and v is its velocity.

## What factors affect the KE of more than one wheel?

The KE of more than one wheel can be affected by several factors, including the mass and velocity of each wheel, as well as the number of wheels and the efficiency of the system. Other external factors such as friction and air resistance can also affect the KE of the system.

## Why is the KE of more than one wheel important?

The KE of more than one wheel is important because it is a measure of the energy being produced and used by a system. This can be useful in understanding the performance and efficiency of vehicles and machinery, as well as in designing and optimizing these systems.

## How can the KE of more than one wheel be increased?

The KE of more than one wheel can be increased by increasing either the mass or velocity of the wheels, or by increasing the number of rotating wheels in the system. However, it is important to consider the limitations and safety implications of increasing the KE of a system.

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