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Homework Help: 2 questions regarding circular motion and Newton's 1st Law

  1. Dec 17, 2014 #1
    Hey, I'm an adult who finally realized that physics is great and tries to recall (or rather learn for the first time) what he learned at the school. I've been reading some basic things around. It's not really a homework question, I'm just trying to understand the laws here.

    1. I know that if a car drives in a circle with a steady velocity, it accelerates towards the center of the circle. For some reason I can't understand the thing about the acceleration, I mean it is still driving with a steady velocity, so where is the acceleration? Doesn't the acceleration imply that it'd speed up? And why is the acceleration always 90 degrees from the velocity direction? Why not 45 degrees or some other number?

    2. Newton's first: as I understand, if I drop a lemon on the table, since the force it encounters is balanced, it (the lemon) still moves in a straight line with a steady velocity...? It's very counter intuitive... does my lemon come to the rest, or is it still moving? And then when I think of the relativity, Newton said that if an object is at rest it will stay at rest, but is there anything in the universe that actually is at rest? Is my lemon at rest in relation to the earth, or is it still moving? It freaks me out...

    Thanks in advance and sorry if I posted it in the wrong place...

    All the best,
  2. jcsd
  3. Dec 17, 2014 #2
    Hi. Welcome to the forum :)

    Probably you've seen acceleration defined as the change in velocity or as the change in motion. Since velocity is a vector, that has both magnitude and direction, an acceleration can cause a change in the magnitude of the velocity (speed up or slow down) or a change its direction (or both).

    In circular motion at constant velocity, there is indeed an acceleration because there is a change in the direction of ##v##.

    Think about a toy car. You don't necessarily have to exert a force parallel to the ground to make it move. If you push with your finger at an angle of 45º on the toy car, you'll still make it move (it'll be subjected to an acceleration). Now, if you imagine the car of your example being pushed at an angle of 45º from one of the sides (or any angle ##\small{\theta \neq 90º}##), it will have a component of the force making it speed up or slow down (it'll depend on how the force is applied respect to its motion). The only way not to cause a change in the velocity's magnitude, changing just its direction, is by applying a force perpendicular to the car, toward the center of rotation: 90º.

    I'm not sure if I've understood what you mean about Newton's First, but Newton's Laws just apply in non-accelerating frames of reference.
  4. Dec 17, 2014 #3


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    Non-zero acceleration just means that there is a change in velocity. Often, this is in the form of slowing down or speeding up. But since velocity is a vector quantity (it has a magnitude and direction) it also takes acceleration to change the direction of the velocity (because velocity is still changing). If there were no acceleration it would just go off in a straight line. Uniform circular motion is a prime example of how the magnitude of the velocity can be unchanged by acceleration.

    The force on the lemon is not unbalanced. There is one force on the lemon, and an equal and opposite force on the Earth, so the net force on the Earth-lemon system is zero, (meaning the center of mass of the Earth-lemon system is unaccelerated) but the net force on the individual lemon is not zero (and so the lemon is accelerated).

    "An object at rest stays at rest"
    More generally, an object with a certain velocity will maintain that velocity (unless a force acts). "At rest" is just a special case where the velocity is zero. And also, when you are speaking of an object's velocity, it only makes sense if you are speaking of the velocity relative to something. The idea of "absolute motion" doesn't make sense, you have to specify (or at least know) what the velocity of the object is relative to.
    (Similarly, it only makes sense to say an object is at rest relative to something else.)
    Last edited: Dec 17, 2014
  5. Dec 17, 2014 #4


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    Wow, great questions!
    1. Circular motion is complicated because the car on a curve is constantly changing direction. If you picture the car at the moment it is going straight north but turning west, then the car is accelerating in the west direction. It's component of velocity in the west direction is increasing and acceleration is the rate of change of velocity. Unfortunately you can only understand why the increasing speed to the west and decreasing speed to the north when at an arbitrary point in the curve amounts to acceleration toward the center of the circle through the twin mathematical detail devils of trigonometry and calculus.

    Another approach I used in teaching high school physics is to fill a plastic pail with water, tie a string to the handle and swing it around in horizontal circular motion. I only got the kids wet once in 30 years! Think about the water. It will move in a straight line at constant speed unless a force acts on it. The force is supplied by the pail through me pulling on the string. The string can only be pulled toward my hand at the center of the circle so there is a force on the water acting toward the center of the circle. And that means the water is accelerating toward the center according to F = ma. Why does the water stay in the pail?

    2. The forces on the lemon are pretty much balanced when it is freely falling but during the collision with the table, the table pushing on the lemon (because the lemon is pushing on the table) causes the lemon to decelerate. Since acceleration = change in velocity/change in time, the acceleration will be quite large if the lemon is hard and it will stop suddenly.

    If an object is at rest (with respect to an observer), it will remain at rest (...) unless acted upon by an outside force.
    When my Education professor, who had taught high school physics, used this as an example in a large lecture theatre, I showed my interest by placing some Mexican Jumping beans on his counter before the next class. It was an unfair joke because he couldn't go into friction and Newton's third law with this class of mostly non-physics students.
  6. Dec 17, 2014 #5


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    .. which is a contradiction, and the source of the confusion. It is circular motion at constant speed.
  7. Dec 17, 2014 #6
    True. (:
  8. Dec 17, 2014 #7


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    No, if they were balanced it would not accelerate towards the table.
    Before collision, there's no force from the table, so the lemon accelerates downwards. After collision (and all motion has ceased), the forces balance. During collision the forces situation can be quite complicated, but certainly the upward forces on the lemon from the table will at times be greater than mg, creating a sufficient upward acceleration to bring the lemon to rest.
    At elementary level physics, one usually avoids getting into the details of collisions by looking at the bigger picture: momentum and energy. The first is the integral of the force over time, while the second is the integral over the distance through which the force advances. In 'completely inelastic' collisions, the force is considered arbitrarily large for an infinitesimal period of time. This is of course an idealisation, but it works if you ignore the details of the force profile and only deal with momentum. In elastic collisions (completely or partially), the force will be finite and act over a nonzero time interval, but you still don't know how it varies over that time in general. Depending on the circumstances, you could take it to be like a spring, or a constant force, or whatever.
  9. Dec 18, 2014 #8
    Wow, thank you all! You are great, very helpful.

    1 is clear for be now, thanks.

    But 2 still puzzles me. So when I drop the lemon, it accelerates towards the table. When it hits the table, the lemon accelerates upwards - in the opposite direction from it's velocity direction. That is why it stops falling. But does it come to the rest? According to Newton's 1st the lemon will continue to move at the constant velocity until it encounters an unbalanced force, the force from the table is balanced though, so is the lemon still in motion or not? And why? ... unless the force from the table brings the velocity of the lemon to 0 m/s (aka. to the rest), so the lemon still moves with the constant velocity, which is 0 m/s...?
    The confusion comes from one article on the website I read, where they wrote that since the lemon didn't encounter the unbalanced force it still continues to fall... again, quite counter intuitive... any thoughts? Is what I read wrong or I just don't get it?
  10. Dec 18, 2014 #9


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    The lemon does encounter an unbalanced force.
    I've seen this misconception before; it usually arises from Newton's "equal and opposite force" law. The table exerts an upward force on the lemon, and the lemon exerts a downwards force on the table (with an equal magnitude). But on the lemon itself there is briefly an unbalanced force (until it comes to rest).
    The article was wrong.
  11. Dec 18, 2014 #10
    Thanks so much!
    Can you also tell me more (or send me to some article) about this brief unbalanced force that meets my lemon and makes it lose the magnitude in velocity, makes it go to rest?

    If I dropped something as heavy as the upward force of the water into the water, when it hits the water it would meet an equal force and so it would continue to move downwards with the same velocity as it had when it hit the water. Right?

    But when my lemon hits the table it stops. I can see that I'm missing some unbalanced force that makes my lemon stop. What is it?

    Then again if I drop a tennis ball on the table it would bounce, is it because the force of the table is stronger than the force of the falling ball?

  12. Dec 18, 2014 #11
    Maybe having a look at information about energy and momentum can be helpful in getting an idea why there is an unbalanced force.

    In your examples, the unbalanced force produced at the moment of collision is always there, whether the object rebounds or not. If you drop a lemon over someone's head from two different heights, let say 2 cm and 2 m above it, in either case the lemon probably won't rebound but in one case the unbalanced force will cause more pain than in the other one.

    Approaching those situations as some amount of energy that needs to go somewhere and/or a change in momentum that has to occur over a very short period of time (the duration of the collision), rather than just a motion in the opposite direction, may be useful.
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