10-Oct-2016: Centripetal Force with a Motor

Apparatus: An electric motor mounted on a surveying tripod, a long shaft going vertically up from the shaft, a horizontal rod mounted on the vertical rod, a long string tied to the end of the horizontal rod, a rubber stopper at the end of the string, and a ring stand with a horizontal piece of paper or tape sticking out.

Purpose: Find the relationship between θ and ω, and compare the theory value of ω and the experiment value of ω.

Model: ω=2π/t, mrω^2=F, cosθ=(H-h)/L, F=tanθmg, r=tanθL+R
ω is the angular speed of the stopper, θ is the angle between the string and vertical, t is the period of the rotation, m is the mass of the stopper, H is the heigh of the rod, h is the heigh of the stopper, L is the length of the srting, F is the centripetal force, r is the radius of the rotation, and  R is the length of the rod.

Process: Our professor set up the apparatus as showed on the photo below.

    We determined the heigh of the rod and the length of the string before it started. Then, professor turn on the motor. The stopper started rotating. By changing the power of the motor, we collected the different heigh of the stopper h and the time of 10 rotations the stopper 10t.
    We used 
                                     ωtheory=2π/t 
to find out the theory value of angular speed, and we used 
                           ωexperiment=(tanθg/(sinθL+R))^(1/2), θ=cos^-1((H-h)/L) 
to find out the experiment value of angular speed.
    Compare the ωtheory and ωexperiment and find out the off between them.
    

    
    There are some error during the expriement such as the rod (meter strick) does not keep horizontal when it is rotating. The rod's changing makes the heigh H different than we think, so the angle θ is different, the radius is different, and the centripetal force become different.
And when we determine the heigh of the stopper, it makes the stopper slower because it hits the paper. They make ωexperiment. The slower speed make ωtheory larger.