# Moment of Inertia: Car vs Sphere

• Heyxyz
In summary, the conversation discusses the calculations for the energy of a ball and a car with small wheels. The equations for both are given, with the car having a slightly larger coefficient. However, the weight and mass of the car are considered more important factors than the wheels, which can be ignored for the purpose of calculating energy. The car's energy should be based on its body, not the wheels.
Heyxyz
Homework Statement
A toy car and a solid metal sphere are rolled down an incline, why does the car reach the bottom first?
Relevant Equations
KE (total) = KE + KE (rotational) = 1/2mv^2 + 1/2Iw^2

Sphere: I = 2/5mr^2

v = wr

w = omega
Hello,

I tried to put it in an equation, but it didn't really work out. In this situation, the car was about the size of a model, and, while not exact, the radius of each wheel couldn't have been more than like a centimeter. Conversely, the ball was like twice the size of the car and had a diameter of 10 - 15 cm.

Ball:

=1/2mv^2 + 1/2I(V/R)^2, I = 2/5mr^2

= 1/2mv^2 + (1/2)(2/5)(m)(r^2)(v^2/r^2)

=7/10mv^2

Car:

Since wheels are practically cylinders, I figured I = 1/2mr^2. There are four wheels, so 4 * 1/2mr^2 = 2mr^2

=1/2mv^2 + 1/2I(V/R)^2, I = 2mr^2

= 1/2mv^2 + 2m(r^2)(v^2/r^2)

=1/mv^2 + mv^2

= 3/2mv^2I don't understand where I'm going. If I follow my above equations, it would appear that the ball reaches the bottom sooner due to the smaller coefficient, but I know that isn't true. Maybe the smaller radius of each wheel has something to do with it?

Thank you.

Delta2
Heyxyz said:
Since wheels are practically cylinders, I figured I = 1/2mr^2
I doubt the car body is massless. I would take it as being far more massive than the wheels.

That's true. Does the car's mass make a difference? I know mass is there, but I just figure it could be ignored (we weren't given masses). I might sound like a fool, but I don't even know how an external mass such as the car would affect the wheels of their velocity.

Heyxyz said:
That's true. Does the car's mass make a difference? I know mass is there, but I just figure it could be ignored (we weren't given masses). I might sound like a fool, but I don't even know how an external mass such as the car would affect the wheels of their velocity.
The weight of the car is the primary driving force, much more important than the weight of the wheels. And the mass of the car does not rotate, so all its KE goes into linear motion.
Consider the wheels to be so light in relation to the car that they are irrelevant.

Delta2
Okay. In other words, the wheels essentially exist so we can ignore friction, and my car's energy should be based on the body of the car rather than the wheels. That actually makes a lot of sense. Thank you.

Delta2
Heyxyz said:
Okay. In other words, the wheels essentially exist so we can ignore friction, and my car's energy should be based on the body of the car rather than the wheels. That actually makes a lot of sense. Thank you.
Correct.

## 1. What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is the sum of the mass of an object multiplied by the square of its distance from an axis of rotation.

## 2. How is moment of inertia different for a car and a sphere?

The shape and distribution of mass in an object determines its moment of inertia. A car, with its irregular shape and varying distribution of mass, will have a different moment of inertia compared to a sphere, which has a symmetrical and uniform distribution of mass.

## 3. Why is moment of inertia important for a car's performance?

Moment of inertia affects how quickly a car can accelerate, decelerate, and change direction. A higher moment of inertia means the car will be more resistant to these changes, while a lower moment of inertia allows for quicker and more responsive movements.

## 4. How is moment of inertia calculated for a car?

Moment of inertia for a car can be calculated by dividing the car into smaller shapes and using the formula for moment of inertia for each shape. These individual moments of inertia can then be added together to find the total moment of inertia for the car.

## 5. How can moment of inertia be changed for a car?

Moment of inertia can be changed by altering the shape or distribution of mass in a car. For example, adding weight to certain areas of the car can increase the moment of inertia, while reducing weight can decrease it. Changes in the car's design and materials can also affect its moment of inertia.

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