- #1
dl447342
- 28
- 5
- Homework Statement
- Determine whether spool A in the diagram below will strike the floor to the left of the x, where the x is initially directly below spool A and likewise for spool B.
Determine which of the students is correct in the second picture below and determine newton's second laws.
- Relevant Equations
- Torque = moment of inertia * angular acceleration, net force = mass * acceleration (newton's second law).
I think both spools will land about at the spot x (there aren't any horizontal forces causing them to land away from the x).
Also, I think student 2 might be the closest to being correct, but I'm not sure if they're entirely correct; isn't it possible that force doesn't only go to translational and rotational acceleration (E.g. some force can be used for thermal energy)?
Or maybe student 3 is right too? Isn't that the statement of Newton's second law?
For the equations, I think one should get the following (here ##\alpha## is the angular acceleration of spool A, ##m## is the mass of each spool, and ##a_A, a_B## are the accelerations of the center of masses of spools A and B, ##I ## is the moment of inertia of spool ##A##, ##\tau_{net}## is the net torque on spool A, and ##R## is the radius of spool A):
##I\alpha = RT = \tau_{net}##
##mg - T = ma_A##
##mg = ma_B##