Rotational+Energy+Lab

Students use LoggerPro (or other video analysis software) to study two points on a yo-yo that is falling and not-slipping on a string. The yo-yo is both translating and rotating.
 * Rotational Energy Lab:**

Note: You MUST have the quicktime video loaded on the computer on which you are doing the lab. it is not really "embedded" in the LoggerPro file. If LoggerPro cannot find the video, it will ask you to find it.


 * Center of Mass:**

I have the students graph the vertical position of the center of mass as a function of time and curve fit to a parabola to find its acceleration. The center of mass is accelerating at about 6.6 m/s^2. It is less than free fall becuase some of the initial gravitational potential energy is being converted to linear KE and some is being converted to rotational KE. You may also have your students draw an FBD for the center of mass. Becuase of the upward tension in the string, the net force is less than the weight. The first frame of the video (From LivePhotoPhysics) gives you the mass and radius of the yo-yo.


 * Point on the Edge of the Yo-Yo:**

My lab asks the students to graph the horizontal position of the edge of the yo-yo as a function of time. It asks them to curve fit to the following equation:

Vx = (w o +a t)*R*cos(q o + w ot + a t^2/2)

The formula can be explained as follows:

The function within the first parenthesis represents the instantaneous angular velocity of the yo-yo. I got a better curve fit if I included an initial speed. Though the footage is shot at 30 frames per second, the person must have released the yo-yo in between shots. You need to multiply the instantaneous angular velocity by the radius to find the linear speed at the edge of the yo-yo. You then need to multiply the linear speed by cosine to determine the horizontal component. Once you overlay the curve fit to the function you can see that the point on the edge is doing two things--rotating faster and faster--so the maximum horizontal velocities (both positive and negative) are getting greater and greater in magnitude. It is also changing direction faster and faster, so it goes through x=0 faster and faster--so you have a linear function modulated by a cosine function. To be honest, I am not sure how many of my students really "got" this, but it was worth a shot. One of my students asked if the area under each portion of the cosine function was the same--took me a while, but I realized that it was the distance traveled in 1/4 of a cycle--or the radius. We tried to test this in LoggerPro, but there weren't enough data points.


 * The following files are: word file of lab sheet, pdf of lab sheet, blank LoggerPro template, Sample Data**



media type="file" key="yo-yo_disk2.mov" width="300" height="300" Angular momentum lab I HAVE no handouts as I teach by modeling physics where the lab comes first and the equation comes from the lab. Then we use the equation to do homework. let me clarify the lab. the pendulum is around 300g I use one string through a loop on the lead mass. (it is from a specific heat kit). Because it is one string they only have to burn through one string and the mass will fall into the clay receiver (no bounce). My students always must come up with the independent and dependent. WE draw on linear and when ever there is a collision we use momentum so it is natural for them to invoke momentum before the collision as an independent. we have already derived rotational mass from experiment weeks before and keeping with momentum the dependent is Iw. the slope of the graph is kgm/s/kgmm/s which is 1/m which is the inverse of the radius to the receiver. moving the radius to the other side gives mass*velocity*radius=Iw I have read studies that indicate that humans have a much more difficult time remembering rotation than translational motion so I try to do as many rotational labs as possible. any good rotational platform with low friction can have a clay catcher. I do not want to fire a cannon into the clay as it is not as much fun. They have a great time and laugh at whom ever burns themselves. let me know if you have any other questions.