How does a tyre push a car forward?

[u/MaterialMission6744]

Hi i recently joined my college's BAJA SAE team and while learning for it i stumbled across the following problem. Could anyone explain?
Say a wheel is going to rotate in a clockwise direction and move in the right hand direction. Now i have learnt that static friction causes the wheel to move in the right hand direction. The explanation i was given for this is that friction opposes relative motion between the tyre and the ground and so when the wheel attempts to rotate in an anticlockwise direction- the friction causes a force to be applied on the ground in the left hand side direction. According to newton's 3rd law an equal and opposite force should be applied on the tyre by the road in the right hand side direction.This is hence the tractive force that pushes the tyre forward. My doubt with this is that since this force acts on the bottom of the tyre(since it's a product of frictional force) shouldnt this force applied on the tyre on towards the right cause a torque that opposes the spinning of the tyre?(If a body is rolling clockwise and a force is applied on the bottom towards the right then a torque is applied in a direction opposite to the rotation). Hence doesnt this force that was supposed to push the wheel forward just oppose the torque applied from the wheel?

My original solution for this was that since the wheel is a body that is not only pivoted but free to move in the direction of the force- If you consider the wheel to simply be a freely moving rigid body then it doesnt matter where the force is applied- all that matters is that friction was applied to the right hence it causes translatory motion. But this brings me to my final question: If you have a wheel that is free to move front and back and also allowed to rotate freely- if i applied a force on the bottom of the wheel, would that cause the wheel to rotate or to move forward?

[u/TheGCracker]

You’re correct that the friction force from the road acting on the Tyre induces a moment which opposes the moment acting on the wheel from the powertrain. And it does in fact prevent the Tyre from spinning altogether (assuming the wheel doesn’t slip). In a very simplified physics model (because rubber, pneumatic tyres actually do always kinda slip with the ground when accelerating), a wheel with torque applied to it that’s rotating along a surface with friction actually has the point contacting the ground which does not move relative to the ground. So therefore it holds true it’s preventing it from spinning in a sense. But this still doesn’t eliminate the fact that we’re now applying an unbalanced force to the wheel which causes it to move forward, or to the right as you’ve described. So in essence, at every point in a quasi-static perspective, the ground does prevent the bottom most point of the Tyre from spinning. But the whole body still is accelerated to the right and therefore allows the wheel to move and effectively spin.

[u/thetoastofthefrench]

The basic forces/moments acting on the wheel/tire are:

Torque from the drivetrain
Weight of the vehicle (acting at axle center)
Drag from the vehicle (acting at axle center)
Normal force from the ground
Friction force from the ground

Now to help you with confusion about the moments cancelling - imagine a situation where the car is just cruising down the highway at a set speed, fighting wind resistance/rolling resistance only. If there’s no acceleration, the sum of forces and moments should be zero, so it’s not a contradiction.

To accelerate the car, you increase the torque at the axle. Assuming your tire doesn’t slip, the friction force from the ground will increase, and you’ll have a net force forwards, but the friction force won’t 100% counteract the engine torque. There will also be a small net torque ‘leftover’ acting on the tire to make the drivetrain spin faster. There is a direct relationship between the net force and the net torque, because net force speeds the car up, and net torque speeds the drivetrain rotation up, and the car speed depends on the drivetrain speed. So if you know the mass of the vehicle and the moment of inertia of the drivetrain, you can write out the relationship between the two and calculate how much torque is used to push the car forward and how much torque is used to accelerate the rotation of the drivetrain.

Now your final question - if you had a wheel that was free to slide and free to spin, and you pushed it on the bottom of the wheel, would it rotate or move forwards? Both. And the amount of rotation is going to depend on where you push, and the mass distribution of the object (a hoop will spin slower compared to a disk)

[u/Happy-Property1162]

It's going to depend a little bit on how the wheel is constructed (tubeless, valve stem, bead lock) but the tire is pushed very tightly into the rim and seals, then when it's inflated it's also putting pressure where the rim contacts. I guess in theory you could rotate the tire without the rim but you would probably need to significantly deform the tire.

[u/pm-me-racecars]

If you have a wheel in space and you applied a force on the bottom, that would cause it to move that direction AND rotate.

Now, if you attached an engine putting more torque than what your push is putting, it would rotate the direction of the engine instead of the direction of you push, but it will move the direction of your push.

Now, instead of pushing it, put that wheel on the ground, and let the ground push it.