What is the force causing circular motion to move upwards?

This is known as centripetal acceleration). In summary, as the angular velocity of a weight on a rope increases, the radius of the orbit also increases due to the outward acting centrifugal force. However, mathematically, the upward movement of the orbit is caused by the increase in tension in the string that acts in the vertical direction, counteracting the force of gravity and resulting in the weight moving upwards. This can be seen by looking at a free body diagram and observing the changes in tension as the mass rotates.
  • #1
bstruss
I understand elementary physics pretty well and can easily conceptualize the following but cannot understand part of the math. Someone starts swinging a weight overhead on a rope and, of course, as the angular velocity increases the radius tries to increase. This is witnessed as the orbit moving higher up until the rope becomes more perpendicular with the axis of rotation. I understand that as omega increases the increasing centrifugal force acts outward on the weight, normal to the axis of rotation (thus trying to increase the radius). What I cannot understand mathematically is what component of the force is acting in the upward direction that causes the weight orbit to move upwards. Can someone show this using the proper equations?

Thanks for any help
Bailey--
 
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  • #2
Welcome to the forums!

If you look at the mass/string from the side and draw a free body diagram, you'll see it.

You will have gravity acting on the mass, downward.
You will have the centrifugal force acting straight outward.
And you will have the tension in the string acting in the direction the string is pointing.

If the mass is not rotating, the tension in the string entirely cancels the force of gravity.

If the mass is rotating, horizontal component of the force of the sting counters the centrifugal force, and vertical component of the string counters the gravity.

For sake of argument, assume that we have the string rotating steadily where there is a -45 degree angle with the horizontal. Assume you then speed the mass' rotation up a little, and look at what is happening before the mass moves any (up or down).

The tension in the string increases to keep it in a circle. Since the tension is acting in both horizontal and vertical directions, and both increase, you now have an unbalanced force on the mass in the +vert direction. That is the force which causes it to rise.

The reason it doesn't rise forever is because as it is rising, the vert. component of the tension is decreasing as the horizontal component is increasing. When the vert. component = gravity, the mass is again in a steady 'orbit'
 

Related to What is the force causing circular motion to move upwards?

1. What is the force causing circular motion to move upwards?

The force causing circular motion to move upwards is called centripetal force. It is a force directed towards the center of the circular path and is responsible for keeping an object moving in a circular motion rather than in a straight line.

2. How does centripetal force work?

Centripetal force works by constantly changing the direction of an object's velocity, forcing it to move in a circular path. This force is created by an inward pull or tension, such as tension in a string, gravity, or friction.

3. What happens if there is no centripetal force?

If there is no centripetal force acting on an object moving in a circular path, it will continue moving in a straight line tangent to the circle. This is known as Newton's first law of motion, also known as the law of inertia.

4. What factors affect the strength of centripetal force?

The strength of centripetal force depends on the mass of the object, the speed at which it is moving, and the radius of the circular path. The greater the mass or speed, or the smaller the radius, the stronger the centripetal force required to maintain circular motion.

5. Is centripetal force a real force or an apparent force?

Centripetal force is a real force, as it is caused by an actual physical interaction between two objects. However, it is sometimes referred to as an apparent force because it is not a fundamental force like gravity or electromagnetism, but rather a result of other forces acting on an object in motion.

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