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

  • Thread starter inv
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  • #1
inv
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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 ?
 

Answers and Replies

  • #2
Lnewqban
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What type of torque are you referring to?
 
  • #3
haruspex
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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.
 
  • #4
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.
 

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