Exploring Velocity & Acceleration Vectors

[jlyu002@ucr.e]

Homework Statement

The diagram shows different phenomena when velocity vector and acceleration vector are on the same graph. The first graph which is pretty simple is when acceleration and velocity are pointing in the same direction. This means that the object's speed is increasing. The second graph shows acceleration pointing up in the y-axis and velocity vector pointing to the right on the x axis. This represents constant speed for the object. I can visually understand the above two demonstrations; however, the next two diagrams really confuses me. The acceleration vector is now in between 0 degrees and 90 degrees pointing diagonally having a x and y coordinate, while the velocity vector is pointing to the right on the x-axis. The last diagram is similar in that the velocity vector is pointing to the right on the x-axis while the acceleration vector is pointing diagonally in between 90 degrees and 180 degrees. In what situation does this actually occur in real life. I can't seem to visualize this phenomena.

Homework Equations

In the book they give an example in which the acceleration is pointing diagonally in between 270 degrees and 360 degrees and the velocity vector in the direction pointing right on the x-axis. This is their explanation. The component of acceleration parallel points along the line of the objects motion, so the speed of the object will change; in particular, the speed will increase, since a parallel points in the same direction as v. The component of a that's perpendicular to v, will make the direction of v change; in particular, it will turn downward(since a perpendicular points downward). Therefore, we'd expect the object to increase in speed as it turns downward. I don't understand the last part, as i cannot see its relative starting point and as i cannot visualize this process.

The Attempt at a Solution

I think it might have something to do with centripetal acceleration, or when an object is curving. I am not really sure.

 

[rl.bhat]

In the third case, it is the circular motion with increasing velocity and in the forth diagram, it is the circular motion with decreasing velocity. At any instant, the acceleration is the resultant of tangential and radial acceleration.

 

[jlyu002@ucr.e]

Is the circular motion uniform, or not uniform, as in the case of a vertical loop, in which it is not uniform, but has centripetal motion.

From what you have said I came to another conclusion, correct me if I am wrong, that the the object in centripetal motion is slowing down or speeding up.

 

[rl.bhat]

It depends on the presence of the tangential acceleration.

 

[jlyu002@ucr.e]

Sorry Rl.bhat for my vaguness. I was addressing my prior post to the answer you gave above. I was wondering if the third and fourth case was due to only uniform circular motion, or non-uniform circular motion.

And lastly, what about for cases in which the acceleration component is in the quadrant 3 and 4?
Would it be the same answers that you gave above except in different order?
Thanks so much for all your help.

 

[rl.bhat]

The third and fourth case is possible only in the non-uniform circular motion.
It is very difficult to grasp the problem without seeing the graphs. Your discriptionsn is not giving the clear picture of the problem. Can you provide the graphs?

 

[jlyu002@ucr.e]

I used the term graph to possibly help visualize the vector components. In the book there is no graph just two arrows that represent the phenomena.

 

[jlyu002@ucr.e]

So basically, on an x-y coordinate system, the acceleration vector is in between 0 degrees and 90 degrees pointing north east, and the velocity component is pointing directly east resting on the x-axis. I was wondering what phenomena this represents in real life and I was also wondering, with the velocity pointing east resting on the x-axis for the next cases, what would it look like when the acceleration is pointing northwest, southwest, and south east. Here are examples of what I know so far. When the acceleration vector is pointing directly west resting on the -x-axis, and when the velocity is pointing directly east resting on the +x-axis the speed of the object is slowing down. The other example is when the acceleration vector is pointing directly north resting on the +y-axis and when the velocity vector is pointing to the east resting on the +x-axis velocity is not increasing and is constant.

For my question I stated above, I know that we can break them apart into vector components i and j; however, I don't understand what that means in real life and what is going on.

 

[rl.bhat]

Well. Here is an example which describes your problem.
Suppose you want to move a roller on a pitch towards east. Either you have to pull it or push it. If you want to pull it, you have to apply the force in the north east direction. So the acceleration is in that direction. If you want to stop the moving roller in the above case, you have to apply the force towards south west direction. The direction of the force changes wnen you push the roller.

 

[jlyu002@ucr.e]

Thanks Rl.bhat for your patience and your help. This helps a lot. I like to visualize physics and applying it to real life situations helps so much.

 

[jlyu002@ucr.e]

Thanks Rl.bhat for your patience and your help. This helps a lot. I like to visualize physics and applying it to real life situations helps so much.

 

[jlyu002@ucr.e]

Cool.

 

[jlyu002@ucr.e]

Velocity changes because it changes direction while the speed stays the same. Nice!