Why Does Centripetal Force Keep Objects at a Constant Distance from the Pivot?

[fisico30]

trivial centripetal force...

hello forum,

a simple, qualitative question.

A centripetal force serves to curve the trajectory of an object (acceleration that only changes the velocity direction, not the magnitude).

But why is the object not pulled inward as well? I can see the turning but not the fact that the obj stays at a constant distance from the pivot.

If the object was a rest, a force towards the center would drag it there. But if the obj rotates, it doesn't. For the fact that it has speed. Is it maybe always trying to "escape" in the straight line, so the distance that it would be pulled in is matched by a distance traveled radially out?

thanks!

 

[mathman]

Is it maybe always trying to "escape" in the straight line, so the distance that it would be pulled in is matched by a distance traveled radially out?

Yes! That is how the moon and various satellites stay in orbit around the earth, and the planets stay in orbit around the sun.

 

[ShawnD]

A centripetal force serves to curve the trajectory of an object (acceleration that only changes the velocity direction, not the magnitude).

But why is the object not pulled inward as well? I can see the turning but not the fact that the obj stays at a constant distance from the pivot.

It's because momentum and energy are both vectors. Even if the object keeps the same rotation speed, a change in direction means a change in momentum, and that means applying a force. Usually when someone says centripetal force, they are talking about this required force.

If you apply even more than the required force, then yes it does move closer to the middle, and it increases the rotation speed in order to conserve momentum and energy (v = wr). Next time you watch figure skating (lol), watch for when the skater spins with their leg sticking out and begins to pull their leg in. As they apply a force greater than the centripetal force, they move their body closer to the center of rotation, and their rotation speed increases. I wish I knew the name of that move since it's a great example of rotational physics.

 

[russ_watters]

An object need not stay at a constant distance from the pivot point of a curve. Orbiting planets, for example, don't, and the total energy stays constant.

 

[fisico30]

hi mathman,
i would like to comment on your good answer:
I get the moon orbiting the earth. The moon is moving fast enough and at the same time free falling, such that it never falls on the ground but continues to fall. Its free fall trajectory matches the curvature of the earth.

But in the case of an object, on a table, rotating in a circle (pivot at the center) because attached to a rope. The object wants to go straight. The rope is a constraint. It cannot extend.

The other example: A rotating object on a table supports from falling another object attached to the other end of the rope . There is a hole in the table and the rope passes through it to connect to vertical object. I can see the body diagrams but it still does not physically make sense...

 

[rcgldr]

A centripetal force serves to curve the trajectory of an object (acceleration that only changes the velocity direction, not the magnitude). But why is the object not pulled inward as well?

Being turned is being pulled "inwards" towards some point perpendicular to the path the object would otherwise be traveling if it wasn't for the centripetal force.

A rotating object on a table supports from falling another object attached to the other end of the rope. There is a hole in the table and the rope passes through it to connect to vertical object.

The rotating object applies a tension force to the rope = m v^2 / r. The hanging object applies a tension force to the rope = m g. If these two forces are equal, the hanging object doesn't move, and the rotating object moves in a circle. If the forces aren't equal, then the rotating object's path is initially a spiral and the hanging object moves up or down. The change in gravitational potential energy of the hanging object is converted into kinetic energy of the rotating object. It's angular momentum is preserved through all of this though. Assuming no friction, then momentum effect cause "over-correction", and the rotating object transitions between spiraling outwards and inwards, while the hanging object travels up and down. I'm not sure of the actual path.

In a two body system in outer space, with gravity as the only force between the two objects, the two objects will each follow a elliptical path or possibly a circular path. There are some animations of this here:

http://en.wikipedia.org/wiki/Two-body_problem