Uniform Circular Motion and centripetal force

[abpandanguyen]

Homework Statement

A body can move in a circle at a constant speed if
a. there is an unbalanced radial force directed inwards.
b. inward and outward forces are equal in magnitude
c. the net radial forces equal the net tangential forces
d. all the statements above are correct
e. none of the statements above are correct

Homework Equations

I think centripetal force is related to this question, but I'm not sure if it is needed to explain it.
F_c = (mv²)/r

The Attempt at a Solution

I tried reading this in my book and looking it up online, but with my thinking, everything seems to be contradicting each other and I am not sure how to process it. All I have gotten from them seems to be that there is a centripetal force towards the axis of rotation that produces a centripetal acceleration with changing velocity, but constant speed. I think there is a radial force inwards, but I'm not sure whether or not to say if it is unbalanced or not?
Help a nub out plox :<

 

[kjohnson]

If you had a inward and outward force that were equal in the radial direction then your Fnet in that direction would equal zero. If the net force is zero in a direction then you can't have an acceleration. Hope that helps direct you in the correct direction.

 

[TagutoAza]

You should try to approach the problem by thinking about it in 2 parts.

The centripetal force is a force that is keeping the particle moving in a circle, the centripetal force is the cause of radial acceleration. However, the actual velocity of the particle is affected by the tangential acceleration, not the radial acceleration. Very much like projectile motion, the x and y components are independent of each other.

Try considering the radial and tangential acceleration separately. Hope this help!

 

[abpandanguyen]

Okay... so if there is equal outward and inward radial forces (it doesn't say radial forces, but by structuring the words like that I think it is implied) there would be no centripetal acceleration? Knowing that, it would thus be not moving? Am I thinking about that right?
If the net radial forces equal the net tangential forces... what does that even entail, I cannot really imagine it very well.
If there was an unbalanced radial force directed inwards would that make nonuniform circular motion?

 

[TagutoAza]

Again, think of them as separate forces.

The radial acceleration keeps the particle going in a circle, it doesn't contribute to the speed of the particle overall. Thus if there are no radial acceleration, the particle will simply move in a straight line.

 

[abpandanguyen]

Sorry, I posted that during your posting.

Okay, so does it not matter if the net radial forces are equal to the net tangential forces since they affect two velocity and acceleration separately?

 

[TagutoAza]

Correct, the net radial forces and net tangential forces affect 2 velocities and accelerations. So it would not matter if they are equal. In fact, the added tangential acceleration will actually speed up the particle!

Also, I would like to correct the earlier statement about the radial acceleration not affecting the speed of the particle overall, it does, simply from the equation a=v^2/R; however a tangential acceleration can also work with the radial to change the speed of the particle. In fact, you can essentially think of it this way: the radial acceleration affects the direction of the particle while the tangential the speed.

 

[abpandanguyen]

I'm also curious about the other options for this question. What would happen if there was an unbalanced radial force directed inwards. would this result in a nonuniform circular motion?

and just to clarify, would the answer be E?

 

[TagutoAza]

The equation for radial acceleration a=v^2/R earlier was a hint to you to the answer. The equation in itself suggests that you need radial acceleration to achieve uniform circular motion. Notice that the very existence of radial acceleration will result in a constant "v^2". In another word, radial acceleration is a type of acceleration that maintains a constant speed but constantly changes the direction of a particle about a center.

So what does tangential acceleration has to do with anything? In the presence of a radial acceleration, which ensures the particle's circular motion and the constant "v^2", the tangential acceleration will further speed up the particle itself, resulting in non-uniformed circular motion. You can think of tangential acceleration as an added acceleration onto the particle to increase its speed.

I apologize if I confused you earlier by stating radial acceleration doesn't contribute to the speed of the particle. What I meant to say was it doesn't contribute to the increasing of velocity (as most will associate acceleration with increase in speed and not change in direction). My language was most definitely not precise enough and probably caused confusion.

Anyways, the answer should be A. Radial acceleration is required for uniformed circular motion.

 

[abpandanguyen]

Alright! Thank you very much for taking time to explain this to me :D I still had the idea fuzzy in my head after your first explanation, but I think I got it with this last bit you just explained, so thanks.