What Do Velocity-Time and Acceleration-Time Graphs Look Like in Circular Motion?

[Illusion3]

Hi guys,

I am very new to the forum (and physics itself). I have only started my O'levels but am a deep physics enthusiast for interesting problems.

When you have circular motion, and you take the displacement from a point on the circle, what type of:

Velocity-time graph
Acceleration-time graph

does it create? I know it has something to do with the graphs creating sine or cosine waves but am not sure why and for which one.

I know it accelerates - and since the speed is the same, wouldn't the velocity be 0 because it goes in circles and ultimately the displacement is 0?

Thanks,

 

[eljose79]

I can provide some insight into the velocity-time and acceleration-time graphs for circular motion.

Firstly, in circular motion, the velocity and acceleration are constantly changing because the direction of motion is changing. This means that the velocity-time and acceleration-time graphs will not be straight lines, but rather curves.

In terms of the shape of the curves, the velocity-time graph for circular motion will be a sine or cosine wave. This is because the velocity is directly related to the displacement, which is the distance from a point on the circle to the center. As the object moves around the circle, its displacement and velocity will change periodically, creating a wave-like pattern.

The acceleration-time graph for circular motion will also be a sine or cosine wave, but with a phase shift of 90 degrees from the velocity-time graph. This is because the acceleration is related to the change in velocity, and since the velocity is at a maximum or minimum when the displacement is at 0, the acceleration will be 0 at those points. This results in a shift in the wave pattern.

Furthermore, you are correct in saying that the velocity will be 0 when the displacement is 0, as the object is momentarily at rest at those points. However, the velocity will also be 0 when the displacement is at a maximum or minimum, as the direction of motion is changing and the velocity is changing from positive to negative or vice versa. This is why the velocity-time graph is a wave pattern rather than a straight line.

I hope this helps to clarify the relationship between circular motion and the velocity-time and acceleration-time graphs. Keep asking interesting questions and exploring the fascinating world of physics!