Physics 4A (03-10-16)
Centripetal Force
Brett Mccausland
Lab Partner:
Purpose
Model the relationship between the angle made by a circular revolving mass and its angular velocity.
Procedure
As seen in the photo of the apparatus we used a tripod stand to hold a meter stick attached to a steel rod with clamps. This steel rod was attached to a motor that caused the meter stick to revolve and the string and mass attached to it. Due to the net force of revolving motion (centripetal force ) the mass while revolving elevated to some angle well call theta . We measured the change in height and the length of the string in order to find this angle . We did this by placing a second stand that had a piece of paper attached to it and raised it to the point at which the mass collided with the paper. We then measured and recorded the height. Before causing the collision between the paper and the mass we recorded 10 revolutions and took the average to find are angular velocity. 
Calculations
As mentioned in the procedure we used experimental data to find a experimental value for angular velocity. The first thing we did is find the angle, we did so by using our measurement of the height of the large tripod stand and the height of the small tripod
Stand and are length. Now that we had a hypotenuse and a adjacent side we were are to find the angle by taking arccosine as seen in the image labeled find angle. terminal velocities.After we found are general formula for are angle we next found are general formula for are angular velocity in terms of theta using summations of the forces in the x and y components as seen in the image above in the yellow highlighted box. There was also one more much simpler way for us to find are angular speed and that was with the data we had from the times we recorded on the amount of time it took for the bob to make a complete revolution. This was are angular velocity in terms of rev/sec in which we then used the formulas listed in the green box to convert to rad /sec. 
Conclusion and Data Analysis
The data in the excel spreadsheet models circular velocity with respect to time vs the circular velocity with respect to change in the height or the change in the angle. Very consistent with what
We would hypothesis based on observation there is a linear correlation between the change in angular velocity and the change in the height at which it rotates. This is explainable based on are force summation equations we wrote out in which show that the more tension added to the string the more force is going to exerted in not just the x component but the y component as well. The force of gravity in the y component stays constant however as the bob increases speed its angle due to a net force in the y component increases, which is due to the tension force, until the point in which it has no net force in the y component and the tension force in the y component is equal to the force of gravity. Inconsistency in the data are evident since there is not a perfect linear fit as seen in the graph of the data. Beyond the propagation of error from the precision of are tools being (+/-) 0.1cm for are lengths and 0.001 seconds in the stopwatch there are several others. The largest error that I observed was that of the apparatus use of a ruler in which was not rigid and was bending due to the force centripetal . This gives more uncertainty in are measurement for the height of the paper on the small stand since the ruler was bending it made for a slightly lower height. Also it could be observed that there was air friction, the disturbed air could be felt if you stood close to the path of the bob as it went by this non negligible force has an effect on are error in are calculations of angular speed.
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