When a vehicle takes a turn is the sharpness viz radius of turn related to the velocity by conservation of angular momentum? If it is so then while going on a straight a line it has infinite radius of curvature so while taking a turn it's velocity must increase as radius decreases by conservation of angular momentum; but that is contrary to general observation. So what am I getting wrong?
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$\begingroup$ The question is not particularly applicable for cars only, the same goes for any vehicle - a bike,a plane whatsoever.My intention is to know whether any external force has any role to play or even in ideal cases( no friction) similar would be the observations or not $\endgroup$– C RayCommented Oct 8, 2018 at 7:25
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$\begingroup$ You might be forgetting the Earth. If you ignore that then conservation rules will appear to be broken. The turning car will have a slight effect on the Earth. $\endgroup$– badjohnCommented Jul 23, 2020 at 8:34
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4 Answers
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Suppose that a car is driving in a circle with constant and speed. In this case its angular momentum about the centre of the circle is conserved because the friction force that keeps it in its track is radial.
If the car drives on a straight line with constant speed then angular momentum is also conserved, with respect to any axis.
In general the car should drive such that its acceleration is radial and falls off as 1/r. Sounds familiar? Indeed, this defines a Kepler orbit.
I neglected relativistic effects and the effects of the curvature and rotation of the Earth.
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the car turn by an outside force (friction in the wheels) which slows down one part more than another. if you were to turn it batman style- by grappling hook to a lamppost I'd imagine that would be the case (not sure though, not an actual physicist)
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$\begingroup$ Well the wheels turn by friction force but the car can change its direction by turning the steering.So I believe the car as a body doesn't seem to be acted upon by any external torque while changing it's direction.isnt it so $\endgroup$– C RayCommented Oct 8, 2018 at 2:59
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Your premise for applying the law of conservation of angular momentum is wrong. The law can be applied if you find an axis about which the net torque on a given system is zero.
In the case of a car taking a turn, the axis location changes from infinity to a closer point. The center of curvature of the car's path is not a valid axis as it changes with time.
If you are a little more specific regarding the motion of the car, it might be possible to locate such an axis, but if you already know the motion of the car, such an axis is of little practical use.
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Angular momentum is given by $mvr$. Angular momentum is a vector quantity.
In this case angular momentum is not conserved in this case as direction of velocity is changing.
answered Jul 23, 2020 at 0:16
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$\begingroup$ The first and third statements are incorrect. Note that angular momentum is an axial vector. $\endgroup$– my2ctsCommented Jul 30, 2021 at 10:30