The discussion centers on the nature of radial acceleration in the context of circular motion, exploring why it is directed towards the center of the circle (centripetal) and the relationship between radial and tangential acceleration. Participants examine the definitions and implications of these concepts, including the role of centrifugal force and the differences in interpretation based on frames of reference.
Participants express differing views on the interpretation of radial and tangential acceleration, and whether centrifugal force should be considered in the context of circular motion. The discussion remains unresolved with multiple competing interpretations present.
Some participants note that the definitions and implications of radial and tangential acceleration may depend on the specific context of motion (circular vs. spiral), which could lead to different interpretations of the terms used.
The direction of radial acceleration is radial, per definition.Athi Sankar said:
Correction: Tangential acceleration is how fast the speed in the direction of motion is changing, not how fast the direction is changing. If the tangential acceleration is zero, and the centripetal acceleration is not, the object will go around in a circle at constant speed; its direction of motion will change continuously. The centripetal acceleration is the one that changes the direction and is perpendicular to the tangential direction which makes it along the radial direction. Remember that the tangent to a circle at a given point is perpendicular to the radius from the center to that point.Athi Sankar said:
And this part is also backwards:kuruman said:
Could it be that the OP confuses direction and magnitude?Athi Sankar said:
Tangential acceleration changes the magnitude (which is the speed) but not the direction of the velocity vector.Athi Sankar said:
Assumr a puck on a frictionless surface attached to a string that goes through a hole in the surface and that the puck is traveling in a circular motion. There is a Newton third law pair of forces between the puck and string, the string exerts a centripetal force on the puck, and the puck exerts a centrifugal reactive force (a reaction to the centripetal acceleration) onto the string. (In a rotating frame, there is a fictitious centrifugal force, but I'm assuming this not what is being asked about).Athi Sankar said:
The "radial" force is the force perpendicular to the velocity of an object, and points towards the instantaneous center of the curved path.Athi Sankar said:
Nugatory said:
Is this common language? When I hear the words “radial” and “tangential” I automatically think of parallel and perpendicular to the position (from some origin), not to the velocity.rcgldr said:
Only in the case of circular motion, but that's what we're talking about in this thread.Hiero said:
I had a feeling you were silently assuming circular motion, but @rcgldr explicitly says:Nugatory said:
With an example of spiral motion! Quite an unusual interpretation of the word radial.rcgldr said:
At every point on the spiral trajectory the path is momentarily approximated by a circular arc (which will not be centered on the center of the spiral). One would often use such a curved tangent arc to determine how to split an acceleration into "radial" and "tangential" components.Hiero said:
I’m familiar with the concept of curvature, but does anyone actually mean that by “radial”...?jbriggs444 said:
Perhaps this discussion can be put in perspective if one considers the expressions for velocity and acceleration in polar coordinates for motion in a plane. Starting with ##\vec r(t)=r~\hat r##, one obtains the general expressions$$\vec v(t)=\frac{d\vec r}{dt}=\dot r~\hat r+r\dot \theta~\hat \theta$$ $$\vec a(t)=\frac{d\vec v}{dt}=(\ddot r-r\dot \theta^2)~\hat r+(r\ddot \theta+2\dot r \dot\theta)~\hat \theta$$Common special cases,Hiero said:
There is radius of curvature, and radial acceleration could be considered as acceleration in the direction of radius of curvature. Radial acceleration is a synonym for centripetal acceleration. Links:Hiero said:
I don't believe so. If you look at post #15, the radial component of the acceleration has two terms. The first term is the rate of change of the radial speed and the second term is the centripetal term. Example: A car is on a rotating platform and the driver pushes on the accelerator pedal along a radius of the platform. The rate at which the speedometer needle rises is a measure of ##\ddot r## and has nothing to do with the centripetal term ##-r \dot \theta^2##. They should not be both lumped together as "centripetal".rcgldr said:
It seems to me like merely a matter of what center you are using. The momentary center of curvature or the center identified in the coordinate system.kuruman said:
rcgldr said:
Take a look at the links I referenced, in the vector diagrams where acceleration is split into normal and tangential components, the normal component is also called centripetal or radial. I only posted links to those two articles as examples but you can find others doing a web search for "radial acceleration" .kuruman said:
I did take a look at the links and I do not disagree with what is said. However, in those links the motion is limited to circular, namely to cases where ##\dot r=0##. My point in #15 and #17 is that there may be another radial term when the motion is not restricted to a circle and that therefore the centripetal term is only part of the radial acceleration, not the whole story. As @jbriggs444 pointed out in #18, this assumes that a fixed center is used to measure angles and radial distances. If one insists that the only radial component is centripetal, then one has to approximate an arbitrary curved path as a succession of arcs ##ds## each being part of a circle with its own radius of curvature and center. However, I am not sure that this description is more advantageous for formulating solutions to problems than the fixed center description.rcgldr said:
The third diagram from the first link (ux1.eiu.edu) shows a changing path, with total acceleration separated into separate components, ##a = a_r + a_t## or ##a = a_c + a_t## where ##a_r## is radial acceleration and a synonym for ##a_c## which is centripetal acceleration. The path would not have to be a circle, it could be an ellipse, spiral, parabola, hyperbola. Consider a car traveling along a winding road with increasing and decreasing radius turns. The car can be braking or accelerating as well as turning while following the curves in the road, with both tangential and radial acceleration.kuruman said:
I was preparing for exams. So I could not reply for a whilekuruman said:
This Explanation was sufficient from my subject point of view and I thank all for taking effort to clear my doubts.rcgldr said:
