0
$\begingroup$

Everywhere I look it says that centripetal acceleration changes the velocity direction. That would mean either the velocity direction changes or the centripetal force direction changes at some point in time. The problem with that idea is that centripetal force is said to always be perpendicular to the velocity.

Something must change direction to cause the other thing to change direction.

$\endgroup$
2
  • 1
    $\begingroup$ I don't quite understand the question. Take gravity as an example. The centripetal force in this case point toward the center. It changes direction because the planet is in a different place. The planet is in a different place because 1) it has velocity 2) it has inertia and 3) it is acted upon by gravity. $\endgroup$
    – garyp
    May 29, 2020 at 11:34
  • $\begingroup$ Gravity pulls from one location and the planet proceeds to a different place. Now the angle between velocity and gravity direction are greater than 90 degrees. The gravity then changes the velocity direction? The velocity and gravity direction must always be 90 degrees. Correct? $\endgroup$
    – Nectac
    May 29, 2020 at 11:45

2 Answers 2

3
$\begingroup$

The problem in your statement:

"Something must change direction to cause the other thing to change direction."

This is not true. To disprove this claim, consider a block moving with a constant velocity on a frictionless surface. We now apply a constant force on the block in the direction opposite to that of the velocity. The block will slow down, stop, and eventually reverse its direction of motion.

This means that we effected a change in the direction of velocity, but the direction of our force was constant. This is merely an illustration of the laws of vector addition.

In very simple terms: force with a constant direction can cause the direction of velocity to change. (However, eventually, they'll point in the same direction. Perhaps this is the source of your confusion.)


Centripetal acceleration and velocity

Consider a particle moving in a circular path with constant velocity. It is agreed then, that the direction of this particle is constantly changing (...although the magnitude is not). This would mean that it's accelerating: something must be causing this change in the direction of velocity. That 'something' being the centripetal acceleration.

Centripetal acceleration is always directed radially, or perpendicular to the direction of the velocity (which is at a tangent to the circle, always). This means centripetal force does change direction constantly: it's always perpendicular to the direction of velocity. Do note that there's no causality here, and nor any one happening first. Centripetal force and its constant direction change is simply a property of how objects in uniform circular motion behave.

enter image description here

I encourage you now to recall the case we took first: a force causing change in the direction of velocity. Look at the GIF, and imagine sitting on the particle and being pulled so that your direction of velocity changes. If looking at the GIF attached also doesn't give you an intuitive feel for the idea, we'll take a look at a real world instance.


Addendum: Pure rotation and centripetal force

If you've studied pure rotation, or the motion of a car tyre, you'll know that the lowest point ('contact point') of the tyre has zero velocity. While the mathematics behind this isn't very relevant here, one question many first-time students of the concept ask is: How is the contact point lifted up? ...an excellent question. It does, after all, have zero velocity, and is the instantaneous center of rotation (ICOR). How can it then rise, to let a different point come in contact with the ground?

This question and your question have similar answers. Although the contact point has zero velocity, its acceleration is non-zero. It's being acted on by centripetal force, which pulls it upward again. Again, in this case, the centripetal force is not changing direction in the single instant (d$t$) when the point is lifted, but still effects a change in the direction of the velocity vector.

$\endgroup$
9
  • $\begingroup$ Thanks @wavion. I have basic knowledge of acceleration and velocity. In your example, a period of time occurs to change the velocity of the block. Any kind of velocity changing acceleration occurs over time be it at an angle or parallel to the velocity. The acceleration magnitude and period determines the amount of change in angle and or speed of the velocity. Centripetal acceleration has no length in time. It’s as if it goes by different rules. “This is simply a property of how objects in uniform circular motion behave.” By rules outside of Newton’s three laws? $\endgroup$
    – Nectac
    May 29, 2020 at 12:47
  • $\begingroup$ No, it isn't a separate law. By definition, Newton's Laws are differential equations. This means that we can analyze situations where they're applicable in d$t$, on infinitesimally small amounts of time. Centripetal force has a constant magnitude, but has a constantly changing direction. It doesn't go by different rules (:P) it simply changes direction at every instant. By 'property of particles in UCM', I meant that all objects in UCM have centripetal force acting on them. I'll clarify that in my answer. $\endgroup$
    – wavion
    May 29, 2020 at 12:59
  • $\begingroup$ If the force changes direction then after an infinitesimally small distance the force direction will not be perpendicular to the velocity direction which it must always be. $\endgroup$
    – Nectac
    May 29, 2020 at 13:07
  • $\begingroup$ Infinitesimally small time interval...and that's the beauty of calculus. It does remain perpendicular at all instants, since $dt \to 0$. It's almost exactly zero, and so it does remain perpendicular. You'll gain a deeper appreciation for this once you study higher level differential calculus :) $\endgroup$
    – wavion
    May 29, 2020 at 13:16
  • $\begingroup$ But even the smallest distance is still a distance. ANY distance and the force-velocity angle has changed. To consider it any other way is ignoring the reality of geometry. $\endgroup$
    – Nectac
    May 29, 2020 at 13:20
0
$\begingroup$

They do both indeed change direction, saying $F_c$ is perpendicular to $V$ only gives their relative direction to each other. The force acts towards the centre, causing the velocity to change direction, the force now acts through the object's new position to the centre and so on and so on.

$\endgroup$
5
  • $\begingroup$ If they both change direction then what causes the change of direction of both? $\endgroup$
    – Nectac
    May 29, 2020 at 11:30
  • $\begingroup$ I see in your second sentence that it's the force that changes direction first. Correct? $\endgroup$
    – Nectac
    May 29, 2020 at 11:38
  • $\begingroup$ @Nectac There is no "first" i this case. Newton's 2nd law tells us that any net force corresponds to an acceleration, but also than any acceleration corresponds to a net force, $$\sum F=ma$$ You may find it intuitive that the net force causes the acceleration, sure, but saying that any of them comes first is not easy to say. They both appear exactly simultaneously - otherwise there would be a (short) moment where you had force without acceleration, and that is impossible according to Newton's 2nd law here and according to how we know the world works. $\endgroup$
    – Steeven
    May 29, 2020 at 12:42
  • $\begingroup$ Thanks @Steeven. I agree. Force, acceleration and velocity are simultaneous. The direction of all three change constantly with circular motion. What changes what? Something causes a change. If the force direction did not change then over time we could calculate the velocity magnitude and direction. Simultaneous actions and the results over time. Centripetal and force and the acceleration go by different rules. Why should it be different? $\endgroup$
    – Nectac
    May 29, 2020 at 12:58
  • $\begingroup$ It's very much a 'chicken and egg' scenario I suppose. But if you think about it, it must be the force that changes first. To enter into circular motion, there must be some force acting towards the centre to begin with so e.g. you turn your tyres, this causes the force to direct to the centre, this causes the acceleration to alter the velocity etc etc. $\endgroup$ May 30, 2020 at 12:05

Not the answer you're looking for? Browse other questions tagged or ask your own question.