When calculating a car's acceleration, is it ok to substitute Torque?

[inv]

Homework Statement

" When calculating a car's acceleration, is it ok to substitute Torque into a= F/m "

Relevant Equations

a= F/m

T= Fr

1. When calculating a car's acceleration, is it ok to substitute Torque into a= F/m


a= F/m
T= Fr


F= T/r


where

a= acceleration,
F= force,
m= mass,
T= Torque,
r= radius,


a= T/rm ?

 

[Lnewqban]

What type of torque are you referring to?

 

[haruspex]

What type of torque are you referring to?

I think there is only one type of torque ; do you mean, where is this torque being measured?
I would also ask where this radius is being measured.

 

[etotheipi]

I agree with @haruspex, it is tricky to say without more context. If we measure torques about some fixed coordinate system, and the car we model as a particle, then if the resultant force on the car is $\vec{F}$ we can write down $\vec{F} = m\vec{a}$ (or with magnitudes, $F=ma$) in addition to $\vec{\tau} = \vec{r} \times \vec{F}$. The latter also reduces to $\tau = rF\sin{\theta}$ if we take magnitudes.

Now if the angle $\theta$ between the $\vec{r}$ vector and the $\vec{F}$ vector is 90 degrees, then $\tau = rF$, like you say. So if all these conditions are satisfied, $\tau = rma$ is I believe valid.

The condition that $\vec{r}$ always be orthogonal to $\vec{F}$ is the most restrictive one here. It means that your equation is fine for something like circular motion, but generally incorrect for most planar motion.