Question

Circular Motion and Gravitation. Section Review (indicated by SR) and Chapter Review (indicated by CR).
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[ SOLVED ]
SR3. Use an example to describe the difference between tangential and centripetal acceleration.
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SR4. Identify the forces that contribute to the centripetal force on the object in each of the following examples:
a, BICYCLIST moving around a flat, circular track
b, BICYCLE moving around a flat, circular track
c, RACE CAR turning a corner on a steeply banked curve

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[ SOLVED ]
CR6. Can a car move around a circular racetrack so that the car has a tangential acceleration but no centripetal acceleration?
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Answer 1

Any ideas?
Forewarning: I'll be going to bed soon. Others will be here, though!

Answer 2

SR3? Good place to start? This seems like one of those questions where spouting definitions will suffice! They're both velocities, buuuut.....

Answer 3

centripetal and tangential acceleration, what is the difference? Let's say you have a ball on a string and you start spinning the ball around in circles. You holding onto the string are providing a force that acts on the ball to keep it in circular motion, if you let go the ball would fly off in a direction tangent to its circular path. This inward force that you provide onto the ball is what provided the centripetal acceleration. Centripetal acceleration is an inward acting vector; it points toward the center of the circle where you are holding onto the string. So the centripetal acceleration is provided by you in the case of a ball on a string and it holds true for any orbiting object around some center point. Something must be holding it in orbit or it would fly away, the thing that holds it in orbit does so through a centripetal acceleration that acts towards the center of the circle. This keeps the object from flying away.

So we are clear, centripetal acceleration is provided by the force the acts to keep the object in orbit around some center point. The faster the object orbits around some center point the greater the centripetal acceleration. If it is orbiting faster, the object exerts more force on the thing at the center that is holding it in orbit and keeping it from flying away. Try it with a ball and a string. As you spin the ball around you faster and faster you can feel the pull on the string increase with angular speed. So the force you feel you also exert onto the string, so it is you pulling on the string that provides the centripetal acceleration, which acts inward in the direction of the force that you are pulling with.

Tangential acceleration is the acceleration of the object in circular motion at a point tangent to the path of that object. Even if the object is orbiting at a constant rate it is constantly changing direction; it is moving in circles after all. Velocity is a vector that represents an objects speed and direction, so even though the speed of the orbiting object may remain the same it's constantly changing direction means it is continually changing velocity over some period of time. A change in velocity over a change in time is an acceleration. So tangential acceleration is really just a measure of the rate at which the object changes its angle while in motion.

Using the ball and string example again, if the ball is at the 12:00 position and is rotating clockwise, then at that instant in time the velocity of that object points tangentially from the 12:00 position towards the right. If you can imagine the ball just stuck in air at the 12:00 position such that the whole plane of orbit is facing you so you can see the object at every position that would be on a clock. If somebody is spinning the ball over their head then imagine you are above looking down from above onto the rotation. Now as it hits 12:00, and you stop time, moving clockwise, it wants to keep moving towards the 3:00, 6:00 and 9:00 positions and then back to the 12:00 position.

At the 12:00 position if you can imagine reaching down from above where you are watching the ball orbit and placing a small arrow on top of the ball you would place the arrow on it such that it pointed from the 12:00 position directly east, so it is pointing completely to the right. That little arrow is the velocity vector of the ball and it is pointing tangentially to the path the ball is orbiting in. Now let time move again and then stop it again at the 3:00 position. Now look down at the arrow you had placed on the ball it should now be pointing completely south, or downwards only.

Maybe the easiest way to imagine the tangent line the ball would like to travel in if let go is to look at it differently. If you draw a circle on a piece of paper such that the center of the circle is exactly at the origin of an x,y coordinate system. Now you have the x line passing though the 3:00 and 9:00 positions of the circle and the y axis going through the 12:00 and 6:00 position of the circle. If somebody asks you to show them the line tangent to the circle at the 90 degree position, 90 degrees from the x axis means we are talking about a point on the circle that would be at the 12:00 position, right where the positive y axis passes through the circle.

OK, the y axis passes through the point where we want to find the line tangent to. When you want a tangent line to a circle the easiest way is to draw a line from the origin out in a radial direction to that point, like the y axis passing through our 12:00 position from the origin where we are going to find the tangent line at that point, and then where that radial line passes out from within the circle if you draw another line that is at a right angle to the line coming from the origin crossing over the circumference of the circle, that line you draw at a right angle to the radial line is the line tangent to that point on the circle. Here's a "cheesy" example of a tangent line. I will type the letter o here in a second followed by the symbol |, this will show a line tangent to a point on a circle at the 3:00 position.
Here it is ( O| ), that little "|" just to the right of the circle is a line that is tangent to the 3:00 point on that circle and you can see that if a line came from the origin and outward towards the 3:00 position it would cross over our "|" line at a right angle to it. That is why I has said that simply drawing a line from the origin to a point on the circle followed by another line that crosses it at a right angle will give you the line tangent to that point on the circle.

Anyway, the point is, an orbiting object if not held in orbit by some inward acting force (centripetal force) will fly away from the orbit in a direction that is tangent to the point where the inward force was removed. So because velocity is a vector that is constantly changing its direction that means the velocity itself is changing all the time. A change in velocity over some period of time is an acceleration. As the object in orbit changes position from the 3:00 to the 6:00 position its velocity has changed by some amount because its tangential velocity at the 3:00 position pointed downward only, and when it is at the 6:00 position it tangential velocity now points directly to the left (west), a change in tangential velocity over some period of time is a tangential acceleration.

So tangential acceleration is, again, for uniform orbiting speed (which need not be the case) a measure of the rate of change in the tangential velocity vector over some period of time. If it is orbiting at the same rate of speed, its tangential velocity will be changing at a constant rate, and changing tangential velocity is tangential acceleration, so the tangential acceleration is going to be a constant value, since acceleration is just a measure of the rate of change in velocity, if the velocity is changing at a constant rate, then it is accelerating at a constant value.

So centripetal acceleration is due to the force at the center of the orbiting object keeping it in orbit and not flying away tangentially from where it was released. This acceleration acts towards the origin because that is where the force that is keeping the orbiting object in orbit is coming from. Tangential acceleration is the rate of change in the tangential velocity over some period of time. Typically the orbiting object orbits at the same speed, but its position is always changing, causing the tangential velocity to be continually changing. Tangential acceleration is a measure of how fast that tangential velocity changes with time.
centripetal and tangential acceleration, what is the difference? Let's say you have a ball on a string and you start spinning the ball around in circles. You holding onto the string are providing a force that acts on the ball to keep it in circular motion, if you let go the ball would fly off in a direction tangent to its circular path. This inward force that you provide onto the ball is what provided the centripetal acceleration. Centripetal acceleration is an inward acting vector; it points toward the center of the circle where you are holding onto the string. So the centripetal acceleration is provided by you in the case of a ball on a string and it holds true for any orbiting object around some center point. Something must be holding it in orbit or it would fly away, the thing that holds it in orbit does so through a centripetal acceleration that acts towards the center of the circle. This keeps the object from flying away.

So we are clear, centripetal acceleration is provided by the force the acts to keep the object in orbit around some center point. The faster the object orbits around some center point the greater the centripetal acceleration. If it is orbiting faster, the object exerts more force on the thing at the center that is holding it in orbit and keeping it from flying away. Try it with a ball and a string. As you spin the ball around you faster and faster you can feel the pull on the string increase with angular speed. So the force you feel you also exert onto the string, so it is you pulling on the string that provides the centripetal acceleration, which acts inward in the direction of the force that you are pulling with.

Tangential acceleration is the acceleration of the object in circular motion at a point tangent to the path of that object. Even if the object is orbiting at a constant rate it is constantly changing direction; it is moving in circles after all. Velocity is a vector that represents an objects speed and direction, so even though the speed of the orbiting object may remain the same it's constantly changing direction means it is continually changing velocity over some period of time. A change in velocity over a change in time is an acceleration. So tangential acceleration is really just a measure of the rate at which the object changes its angle while in motion.

Using the ball and string example again, if the ball is at the 12:00 position and is rotating clockwise, then at that instant in time the velocity of that object points tangentially from the 12:00 position towards the right. If you can imagine the ball just stuck in air at the 12:00 position such that the whole plane of orbit is facing you so you can see the object at every position that would be on a clock. If somebody is spinning the ball over their head then imagine you are above looking down from above onto the rotation. Now as it hits 12:00, and you stop time, moving clockwise, it wants to keep moving towards the 3:00, 6:00 and 9:00 positions and then back to the 12:00 position.

At the 12:00 position if you can imagine reaching down from above where you are watching the ball orbit and placing a small arrow on top of the ball you would place the arrow on it such that it pointed from the 12:00 position directly east, so it is pointing completely to the right. That little arrow is the velocity vector of the ball and it is pointing tangentially to the path the ball is orbiting in. Now let time move again and then stop it again at the 3:00 position. Now look down at the arrow you had placed on the ball it should now be pointing completely south, or downwards only.

Maybe the easiest way to imagine the tangent line the ball would like to travel in if let go is to look at it differently. If you draw a circle on a piece of paper such that the center of the circle is exactly at the origin of an x,y coordinate system. Now you have the x line passing though the 3:00 and 9:00 positions of the circle and the y axis going through the 12:00 and 6:00 position of the circle. If somebody asks you to show them the line tangent to the circle at the 90 degree position, 90 degrees from the x axis means we are talking about a point on the circle that would be at the 12:00 position, right where the positive y axis passes through the circle.

OK, the y axis passes through the point where we want to find the line tangent to. When you want a tangent line to a circle the easiest way is to draw a line from the origin out in a radial direction to that point, like the y axis passing through our 12:00 position from the origin where we are going to find the tangent line at that point, and then where that radial line passes out from within the circle if you draw another line that is at a right angle to the line coming from the origin crossing over the circumference of the circle, that line you draw at a right angle to the radial line is the line tangent to that point on the circle. Here's a "cheesy" example of a tangent line. I will type the letter o here in a second followed by the symbol |, this will show a line tangent to a point on a circle at the 3:00 position.
Here it is ( O| ), that little "|" just to the right of the circle is a line that is tangent to the 3:00 point on that circle and you can see that if a line came from the origin and outward towards the 3:00 position it would cross over our "|" line at a right angle to it. That is why I has said that simply drawing a line from the origin to a point on the circle followed by another line that crosses it at a right angle will give you the line tangent to that point on the circle.

Anyway, the point is, an orbiting object if not held in orbit by some inward acting force (centripetal force) will fly away from the orbit in a direction that is tangent to the point where the inward force was removed. So because velocity is a vector that is constantly changing its direction that means the velocity itself is changing all the time. A change in velocity over some period of time is an acceleration. As the object in orbit changes position from the 3:00 to the 6:00 position its velocity has changed by some amount because its tangential velocity at the 3:00 position pointed downward only, and when it is at the 6:00 position it tangential velocity now points directly to the left (west), a change in tangential velocity over some period of time is a tangential acceleration.

So tangential acceleration is, again, for uniform orbiting speed (which need not be the case) a measure of the rate of change in the tangential velocity vector over some period of time. If it is orbiting at the same rate of speed, its tangential velocity will be changing at a constant rate, and changing tangential velocity is tangential acceleration, so the tangential acceleration is going to be a constant value, since acceleration is just a measure of the rate of change in velocity, if the velocity is changing at a constant rate, then it is accelerating at a constant value.

So centripetal acceleration is due to the force at the center of the orbiting object keeping it in orbit and not flying away tangentially from where it was released. This acceleration acts towards the origin because that is where the force that is keeping the orbiting object in orbit is coming from. Tangential acceleration is the rate of change in the tangential velocity over some period of time. Typically the orbiting object orbits at the same speed, but its position is always changing, causing the tangential velocity to be continually changing. Tangential acceleration is a measure of how fast that tangential velocity changes with time.

Answer 4

I meant acceleration, not velocity... I didn't read it all, but that looks like a good description!

Answer 5

That would be way too long an example though...

Answer 6

I mean, I understand the differences but I can't get them to fit into an example.

Answer 7

Here is his source: http://physicshelpforum.com/showthread.php?t=4056

Answer 8

Again, that's way too long an example...

Answer 9

I took this stuff out and pasted it here... do you think that (paraphrasing it) is enough?

"Let's say you have a ball on a string and you start spinning the ball around in circles. You holding onto the string are providing a force that acts on the ball to keep it in circular motion, if you let go the ball would fly off in a direction tangent to its circular path. This inward force that you provide onto the ball is what provided the centripetal acceleration. Centripetal acceleration is an inward acting vector; it points toward the center of the circle where you are holding onto the string. So the centripetal acceleration is provided by you in the case of a ball on a string and it holds true for any orbiting object around some center point. Something must be holding it in orbit or it would fly away, the thing that holds it in orbit does so through a centripetal acceleration that acts towards the center of the circle. This keeps the object from flying away.

So we are clear, centripetal acceleration is provided by the force the acts to keep the object in orbit around some center point. The faster the object orbits around some center point the greater the centripetal acceleration. If it is orbiting faster, the object exerts more force on the thing at the center that is holding it in orbit and keeping it from flying away. Try it with a ball and a string. As you spin the ball around you faster and faster you can feel the pull on the string increase with angular speed. So the force you feel you also exert onto the string, so it is you pulling on the string that provides the centripetal acceleration, which acts inward in the direction of the force that you are pulling with.

Answer 10

It doesn't seem like your own words...

What you want to do in times like these is take the information, understand it and make it your own, and then spit out what you just learned onto your paper.

How long of a response is required? Is this a short essay or a simpler question?

Answer 11

for example, if a car increases its velocity from 10 mph to 20 mph, it is accelerating. this would be an example of tangential acceleration. a change in velocity is acceleration. in this case, the change is in the magnitude (bigness) of the velocity.

but when a car turns, for example, it has centriepetal acceleration, because for a while it is traveling a circular path and is changing its direction towards the center of that path. in this example, if the car is slowing down or speeding up during the turn, it is also accelerating tangentially as well as centripetally. however, if the speed remains constant, it has 0 tangential acceleration. it still has centripetal acceleration, though, because it is constantly changing direction towards the center of its path.

hope this helps!

Answer 12

Well, I mean to take certain parts out and use them, not plagiarize.
It's just one of those tiny little section reviews at the end of a section.
but it's okay, I think I get the general idea, thanks @theEric

Thanks @nirmalnema that was helpful (:

Answer 13

your welcome

Answer 14

I got ya!

I didn't see you copied and pasted exactly! I see what you were going for :)

Answer 15

Haha, okay :p
Thanks both of you for your help (:

But could you help me in any other problems? >.<

Answer 16

I'd add

"Tangential acceleration is the acceleration of the object in circular motion at a point tangent to the path of that object. Even if the object is orbiting at a constant rate it is constantly changing direction; it is moving in circles after all. Velocity is a vector that represents an objects speed and direction, so even though the speed of the orbiting object may remain the same it's constantly changing direction means it is continually changing velocity over some period of time. A change in velocity over a change in time is an acceleration. So tangential acceleration is really just a measure of the rate at which the object changes its angle while in motion."

Look at that, because you're already looking at the paragraph on centripetal.

Answer 17

So do you feel like you know enough for (SR3)?

Answer 18

Okay....?
Yes, I did edit and type in that it was solved xD

Answer 19

So, just to make sure & sum up everything, an object turning a curve is centripetal acceleration while increasing its velocity is tangential?

Answer 20

So, in turning a curve, you have centripetal acceleration keeping you towards the center. Like, so a car doesn't just slip away! (road friction)

And the tangential acceleration is what you look at if you were driving the car. You'd see tangent to the path. And that long answer makes a good point - even at a constant speed, the tangential velocity changes, because velocity is the combination of speed and \(direction\).

Answer 21

... so yes, I'm right then. :p

Answer 22

Every step of the way you go a little forward and a little into the circle, if you want to look at it like that.

Answer 23

I'd honestly throw you a medal but I can't do both ; w ;

Answer 24

Haha, don't worry about it! I'm not here for those.

You seem right! I couldn't tell from the wording if you saw that turning a curve has both accelerations.

Answer 25

Also, it's important to know that velocity "increase" isn't necessarily required for there to be the tangential acceleration. Do you know what I mean?

Answer 26

Yep! (:

Answer 27

Cool! So (SR4)!

Answer 28

Ehh.... yeah I'm not so sure about that one.

Answer 29

I have general ideas but I think they're wrong...

Answer 30

Centripetal acceleration - the force is whatever keeps it going towards the center. We want to look for what that force could be, since it must exist.

Well, let's go through them!

Answer 31

Haha.... I'm tired so I pictured the bicyclist without the bike...

Anyway, what are your thoughts on the bicycle, first?

Answer 32

LOL.
Well, the bicycle.... umm, the force that is exerted upon it by the bicyclist?

Answer 33

Haha, the bicyclist is on the bike! The bike is the thing holding the cyclist!

On a flat surface, all you really have is friction. That is what is allowing the bike to go towards the center. Friction between the road and the wheels.

Answer 34

The cyclist, well the cyclist is just attached to the bike... So it's the combination of friction and normal force that holds the rider to the bike, which is discussed in part (b) to have centripetal acceleration due to friction.

Answer 35

Sound good?

Answer 36

Uhhhh... might need a diagram there o.o

Answer 37

and I would put the cyclist on next, but I had already started this picture...