# Does gravity effect the centripetal force acting on an object that spins on a string (vertically)?

Update:

That is to say, if I'm spinning something on a string (on a vertical plane), does the centripetal force increase at the bottom of the circle and decrease at the top due to gravity constantly pulling the object downward?

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Does gravity effect the centripetal force acting on an object that spins on a string (vertically)

NO, but it does change the total force. The total force is the vector sum of the centripetal force and the force due to gravity (the weight). They are at right angles.

Centripetal force f = mV²/r = mrω²

weight = mg

total force = √(Fc² + W²)

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• This is only true when the object is moving in a vertical circle. The direction of the centripetal force is always toward the center of the vertical circle. The direction of the object weight is always down. When the object is at the top of the circle, the net vertical force is the sum of these to forces. When the object is at the bottom of the circle, the net vertical force is the centripetal force minus the object’s weight. Let the mass be 10 kilograms. The radius of the circle be 15 meters. Let the velocity= 10 m/s.

Weight = 10 * 9.8 = 98 N

Fc = 10 * 20^2 ÷ 15 = 150 N

At the top of the circle, the net force is 98 + 150 = 248 N

At the bottom of the circle, the net force is 150 – 98 = 52 N

In both of these situations, the direction of the net force is toward the center of the circle. I hope is helpful for you.

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• Gravity field is radial as opposed to the magnetic field produced by the spin

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• think about swinging on a swingset. Clearly, gravity is affecting the movement and preventing the completion of the circle for the rate of movement involved.

There will always be a component of gravity but it does not affect the centripetal force, it simply adds to or subtracts from that force in affecting the overall motion. The gravity component can be tiny relative to the other forces involved and thus can be ignored for many purposes, of course.

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• Yes. A good understanding of what happens requires some careful thinking. Try this.

For an object moving in a vertical circle on a string, the 2 forces on the object are string's tension (T acting radially inwards along the string) and the object's weight (W acting vertically downwards).

During each rotation W remains constant but the magnitude and direction of T change.

Note, the directions of T and W are different except at the top position.

The resultant force (F) on the object is the *vector sum* of T and W.

The centripetal force (C) is the *radially inwards component* of F.

Therefore ‘gravity’ (weight, W) *is* a part of the centripetal force except at the points where the string is horizontal.

The magnitude of C only depends on mass, speed and radius. |C| = mv²/r. Speed is usually fastest at the bottom position but for simplicity imagine speed is constant, so |C| is constant.

At the top, T and W are in the same direction, both down so:

|C| = |T_top| + |W|.

At the bottom, T and W are in opposite directions, T upwards and W downwards so:

|C| = |T_bottom| - |W|

|T_top| + |W| = |T_bottom| - |W|

|T_bottom| - |T_top| = 2|W|

So the tension at the bottom is bigger than the tension at the top by and amount equal to twice the weight.

If the object is moving faster at the bottom than the top, this difference is even bigger.

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• It affects it in only one way. The centripetal force is m v^2 / r

Falling bodies speed up.

If the speed is higher the centripetal force is higher.

The actual force of gravity has no bearing of any sort on the centripetal force. ie " the force required to keep a body moving in a circle caused by the motion of that body."

The NET force acting on the body from all sources remains m v^2 / r at all times.

This net force is made of the force applied by the string and the force applied by gravity.

In some cases there can be other forces as well.

Just note my earlier point that v is not a constant when something is moving in a vertical plane.

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• sure it affects it...but the spinning counteracts those effects when its spinning fast enough

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