Determining a vehicle's translational acceleration from wheel torque

1. Dec 11, 2011

TB123

1. The problem statement, all variables and given/known data

I am trying to figure out how to determine a vehicle's translational acceleration given a torque at the wheels so that I can determine what effect wheel diameter and mass will have on the ultimate translational acceleration.

2. Relevant equations

F = Ma

I*alpha = Torque

I = .5mr^2

3. The attempt at a solution

Torque = I*alpha = .5*m*a*r^3

a = (Torque*2)/(m*a*r^3)

I think I know how to find the translational acceleration of a rolling wheel, but how can I relate this to the total acceleration of a vehicle with a mass?

Also, there are 4 wheels (only 2 are supplied with a torque). Do I need to think about this as well?

Thanks for the help.

2. Dec 11, 2011

JHamm

You do not need to consider there being four wheels, if the wheels do not slip or slide then the magnitude of the velocity at the circumference of the wheel is the same as the velocity of the car.

3. Dec 11, 2011

TB123

How can I incorporate the mass of the vehicle in the equation?

4. Dec 11, 2011

Staff: Mentor

The car's forward acceleration is due to the force of friction between the driving wheels and the road surface. The wheel pushes back on the road, the road pushes forward on the wheel where they meet. For the car, a = F/M.

Use your torque value to determine the tangential force at the wheel/road interface. This will be the same magnitude as the friction force (provided the wheels are not slipping). What's a formula for torque given the applied tangential force and the radius of the moment arm?

5. Dec 11, 2011

TB123

Ok, so just divide torque by the radius to get the force and then apply f=ma. That's easy enough.

6. Dec 11, 2011

rcgldr

This problem appears to be ignoring any angular inertia effects due to the wheels, since it doesn't include any information about the angular inertia of the wheels.

I see you already figured this out, but I'm unable to delete this message.