Trey Seabrooke, Ryan Partain, Daniel Hanna, Tyler Kolby
Title: Rotating Bodies Model
Purpose: to determine the graphical and mathematical relationship among net force, mass, distribution of mass and angular acceleration for a rotating pulley.
Procedure:
1. Obtain all necessary equipment to record data for rotating bodies model.
2. Three sets of data will be recorded: changing the mass of the hanging mass while keeping the pulley mass and radius constant, changing the pulley mass while keeping the pulley radius and hanging mass constant, and changing the pulley radius while keeping the hanging mass and pulley mass constant.
3. Change the mass of the hanging mass for eight data points and record the time it takes the hanging mass to reach the ground from the bottom edge of the pulley each time.
4. Change the mass of the pulley for eight data points and record the time it takes each to reach the ground from the bottom edge of the pulley.
5. Change the radius of the pulley for eight data points and record the time it takes each to reach the ground.
6. Convert data to rate units of rad/s^2 for all three data sets.
7. Graph all three sets of data and linearize as needed.
Data Tables:
Graphs:
Angular Acceleration vs. Net Force
Angular Acceleration vs. Mass (swinging)
Angular Acceleration vs. 1/Mass (swinging)
Angular Acceleration vs. Radius
Angular Acceleration vs. 1/Radius^2
Conclusion:
1. A) Angular acceleration versus Fnet is linear. Mass and radius of the pulley are held constant
at: .0241 kg and 11.25 cm respectively.
Angular acceleration versus Mass of pulley is inversely proportional: y vs. 1/x to linearize. Mass
of hanging mass and pulley radius are held constant at: .0908 kg and 11.25 cm respectively.
Angular acceleration versus pulley radius is inversely proportional: y vs. 1/x to parabolic relation:
y vs. 1/r^2 to linearize. Mass of the hanging mass and mass of the pulley are held constant at: .
0908 kg and .1991 kg respectively.
B) Angular acceleration versus Fnet is related by the equation: α=(32.09rad/Ns^2)Fnet + 8.2
rad/s^2.
Angular acceleration versus 1/ mass of pulley is related by the equation: α=(1.02radg/s^2)1/M(s)
+ 10.60radg/s^2.
Angular acceleration versus 1/ pulley radius squared is related by the equation:
α=(827.8radcm^2/s^2)1/radius^2 -24.6radcm^2/s^2.
C) These equations can be generalized by the equation: α=r(pulley)Fnet/kmr^2 or α=torque/
inertia.
2. The Rotating Bodies Model allowed our group to determine the graphical and mathematical
relationship among net force, mass, mass distribution and angular acceleration for a rotating
pulley. This rotational motion relates to Newton's laws of motion in that a force is acting upon the
pulley to cause motion of the hanging mass at certain accelerations. The equation Fnet=ma
developed by Newton is also related through the rotational equivalent: torque=inertia(α).
