Apr-14-2015. Lab 9 : Centripetal force with a motor

The apparatus is described below. As the motor spins at a higher angular speed w, the mass revolves around the central shaft at a larger radius and the θ increases. 

our job is to come up with a relationship between w and θ . 
1. we can get the θ from looking at the right triangle with hypotenuse L and height (H-h)s. like the picture. we got the θ= cos^(-1)(H-h/L) . 

2. we can get w from timing how long it takes for the stopper to make 10 revolutions around the shaft.

we measured the L= 1.654m, R= 0.97m, H= 2m by the meter ruler.


3. we can get h by putting a horizontal piece of paper or tape on a ring stand and slowing raising the piece of paper of paper until the stopper just grazes the top of it as it passes by.

then, we got 5 sets of different data to test our model by collecting values of h at a veriety of values of w.
In addition, we calculated 5 sets of different w and θ .





Here is the force diagram:

we got the relationship between w and θ(we already know the R= 0.97m, L= 1.654m, and g= 9.8m/s^2).
set the equation of the relationship between w and θ to y = x. 

then, we put the 5 different θ into this equation to get 5 new w. Now we got the y which means 5 sets of w from timing how long it takes for the stopper to make 10 revolutions around the shaft, we got the x which means 5 sets of w from that we put the 5 different  θ which we calculated from θ=cos^(-1)(H-h/L) into the equation of the relationship between w and θ.  

open the Excel, input all data and make both y and x square. then linear fit the graph. 





From the picture, we got y = 0.9827x. we could see the slope is 0.9827 which means y is almost equal to x.















For this lab, we find the relationship between w and θ . and we got 5 sets of data to test our model by collecting value of h(which we could calculated the θ) at a variety of values of w. the final result y= 0.9827x shows that w will increase with the θ's increase.