# Calculate Torque for Acceleration: 4-Wheel Car with 1000kg Mass & 12m/s Velocity

• michael7777
In summary, the conversation discusses the specifications of a car with 4 wheels and one motor, including the total mass, weight of each wheel, and effective frictional force. The question is posed of what torque is required to accelerate the car at 12m/s from rest, with a possible solution provided. Suggestions are also made to consider the moment of inertia for a more accurate calculation. A helpful website is mentioned as a resource for further understanding.
michael7777
I wasnt sure where to post my question. Here goes:

I have a car with 4 wheels and one motor.
The motor drives an axle connected to the back wheels.
The total mass of the car is 1000kg
Each wheel weighs 20kg and is a solid cylinder
The effective frictional force is 0.2
The radius of the wheel is 0.5m
The radius of the axle is 0.05m

If I would like to accelerate at 12m/s from rest:
What is the required torque on each wheel?
What is the required motor torque?

Here is my lame solution which I think is pretty incorrect:
F = ma * m/g + um
Fwheel = (ma * m/g + um) / 4
Twheel =( (ma * m/g + um) / 4 ) * radius
Twheel = ( (1000*12 * 1000/9.8 + 0.2*1000) / 4 ) * 0.5
Twheel = 153086.2 Nm
Tmotor = 4*Twheel = 612344.9 Nm

I think maybe you need Io = (MR^2) / 2
But i don't know

Last edited:
how to apply it to the problem

I would approach this problem by first defining the variables and equations needed to calculate torque for acceleration.

Torque, denoted as "T", is defined as the product of force and the distance from the pivot point to the point where the force is applied. In this case, the pivot point would be the center of the wheel and the force would be the frictional force between the wheels and the ground.

The equation for torque is T = F x d, where F is the force and d is the distance. We can also use the equation T = I x alpha, where I is the moment of inertia and alpha is the angular acceleration.

To calculate the required torque on each wheel, we need to first calculate the force acting on each wheel. This can be done by using Newton's second law, F = ma, where m is the mass of the car and a is the acceleration. In this case, the acceleration is 12m/s^2. So, the force acting on each wheel is F = (1000kg)(12m/s^2) = 12000N.

Next, we need to calculate the distance from the pivot point to where the force is applied. This can be done by using the radius of the wheel, which is 0.5m. So, the torque on each wheel would be T = (12000N)(0.5m) = 6000Nm.

To calculate the required motor torque, we need to consider the fact that the motor is connected to the axle, which has a smaller radius than the wheel. This means that the torque required at the motor would be greater than the torque required at the wheel. We can calculate the torque at the motor by using the equation T = I x alpha, where I is the moment of inertia and alpha is the angular acceleration.

The moment of inertia, denoted as "I", is a measure of an object's resistance to changes in rotational motion. For a solid cylinder, the moment of inertia is given by I = (1/2)mr^2, where m is the mass and r is the radius. In this case, the mass of each wheel is 20kg and the radius is 0.5m. So, the moment of inertia for each wheel is I = (1/2)(20kg)(0.5m)^2 = 2.5kgm^2.

## 1. What is torque and how is it related to acceleration?

Torque is a measure of the force that causes rotational motion. It is related to acceleration through the equation T = Iα, where T is the torque, I is the moment of inertia, and α is the angular acceleration.

## 2. How do you calculate torque for a 4-wheel car with a 1000kg mass and 12m/s velocity?

To calculate torque, you will need to know the moment of inertia of the car, which can be calculated using the formula I = mr2, where m is the mass of the car and r is the radius of the wheels. Once you have the moment of inertia, you can use the equation T = Iα to calculate the torque.

## 3. What are the units of torque and how are they measured?

The unit of torque is Newton-meters (Nm) in the SI system. It can also be measured in pound-feet (lb-ft) in the imperial system. Torque is typically measured using a torque wrench, which applies a specific amount of force to a lever arm and measures the resulting torque.

## 4. How does torque affect the acceleration of a car?

Torque is directly proportional to acceleration, meaning that the greater the torque applied, the greater the acceleration. In the case of a 4-wheel car, the torque applied to the wheels is what causes the car to accelerate.

## 5. What other factors besides torque and mass can affect the acceleration of a car?

In addition to torque and mass, the acceleration of a car can also be affected by factors such as the engine power, aerodynamics, and frictional forces. These factors can either increase or decrease the acceleration of the car.

• Introductory Physics Homework Help
Replies
33
Views
10K
• Classical Physics
Replies
15
Views
2K
• Introductory Physics Homework Help
Replies
16
Views
2K
• Introductory Physics Homework Help
Replies
6
Views
1K
• Mechanical Engineering
Replies
8
Views
4K
• Electrical Engineering
Replies
15
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
3K
• Mechanics
Replies
4
Views
3K
• Mechanical Engineering
Replies
2
Views
4K
• Introductory Physics Homework Help
Replies
3
Views
1K