# Relationship between tension and frequency circular motion

### Uniform Circular Motion Lab

Circular Motion Lab Relationship between the centripetal acceleration and the In order to eliminate components of the tension force, we are assuming that the and radius will be affected by a negative slope when compared to frequency. Yes, it is proportional to the radius of orbit. However In the second equation, force and radius are directly proportional if mass and frequency are held constant . Both relationships are valid, depending on which variables are being held constant. . Does varying centripetal force produce circular motion?. Circular Motion – centripetal force, centripetal acceleration, angular speed, radians, linear velocity. f is the frequency of the rotation in hertz (Hz). forces in different settings it can be gravity, friction, tension, lift, electrostatic attraction etc .

The controlled variables in this lab are the mass stopper that is experiencing the centripetal acceleration and the radius of spinning motion. Other variables such as the time it takes to complete one revolution can vary depending on a variety of reasons. The mass of the hanging weight is an independent variable, which varies depending on the number of washers that we tie to the end of the string. In order to eliminate components of the tension force, we are assuming that the stopper is rotating perpendicular to the plastic straw please refer to figure 1 for further explanation.

Equations Uniform Circular motion equation. The other two variables such as mass of the stopper and radius will be affected by a negative slope when compared to frequency. The math within our lab report are based on the grounds that the stopper is exactly perpendicular to the plastic straw. The lab is done through the use of a string that has one end tied to a rubber stopper and the other tied to a number of washers. After, we used a meter stick to mark out our fixed radius position by sticking a piece of tape on to the string.

### 1 Circular Motion Circular Motion Lab Relationship between the

The plastic straw is then spun by the hand until the marking on the string has moved to directly under the straw and is no longer fluctuating in position.

Notice the change in radius. Data Analysis The data we collected shows that as the number of washers increase, the rubber stopper needs to be spun faster in order to keep the radius of the circular motion constant.

It also verifies that the period will be smaller if the centripetal force increases, and that these two variables have an inverse ratio. As shown we have 3 time trials of each difference tension force, this helps with the elimination of errors that can be caused when conducting the lab. The graph shows a linear slope of 0. The graph also shows centripetal force well in to the negative, which is the result of using smaller than 1 numbers on a log graph, therefore the data is deemed feasible.

The timer could have also stopped the time before or later when the experiment was being done. To solve this problem, the counter could hold a paper on the edge of the motion.

As the stopper would be spinning, every time it hit the paper, it would count as one. Being able to hear 20 hits on the paper would give an accurate result of time. Another error could be that of the speed at which the string was spinning at.

## Homework Help: Circular Motion of a spinning mass

The speed was not constant for the entire motion, since the string would sometimes be changing radius. In this case the rubber stopper wanted to move in straight, however due to inertia, the stopper moved in a circular motion.

This net force has the special formand because it points in to the center of the circle, at right angles to the velocity, the force will change the direction of the velocity but not the magnitude.

It's useful to look at some examples to see how we deal with situations involving uniform circular motion. Example 1 - Twirling an object tied to a rope in a horizontal circle. Note that the object travels in a horizontal circle, but the rope itself is not horizontal.

If the tension in the rope is N, the object's mass is 3. As always, the place to start is with a free-body diagram, which just has two forces, the tension and the weight. It's simplest to choose a coordinate system that is horizontal and vertical, because the centripetal acceleration will be horizontal, and there is no vertical acceleration.

**Centripetal Acceleration & Force - Circular Motion, Banked Curves, Static Friction, Physics Problems**

The tension, T, gets split into horizontal and vertical components. We don't know the angle, but that's OK because we can solve for it. Adding forces in the y direction gives: This can be solved to get the angle: In the x direction there's just the one force, the horizontal component of the tension, which we'll set equal to the mass times the centripetal acceleration: