tummychow
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1. What happens when two spinning disks collide?
Suppose you have two flat, thin disks with uniformly distributed masses m1 and m2, moving at angular velocities ω1 and ω2. the two objects are brought together edge to edge, ie they collide. obviously as a result of this collision, the objects' angular velocities change. in order for such a change to occur, a torque must be applied. what I don't know is, where is the torque coming from that initiates this change, and what is the equation that describes that torque? it's an entirely conceptual question.
The usual suspects:
T = r x F (torque = cross product of object's position and the force)
ω = α t + ω0 (angular velocity = angular acceleration x time plus initial angular velocity)
beyond this, I'm not sure what other equations apply.
it's conceptual, so I've mostly been muddling it out by deductive reasoning. if two objects are in contact, their circumferences are moving at velocities v1=ω1 R and v2=ω2 R. If these two velocities are equal and in opposite directions, like gears, then (based on real-life observation) they should exert no torque on one another.
if their velocities are not equal in this fashion, then some force is exerted by one object on the other, to adjust the other's velocity towards this equal velocity. theoretically, the force should be proportional to the difference between the current and target velocities. but since i have no idea where this force comes from, that's about where my reasoning came to a halt.
Suppose you have two flat, thin disks with uniformly distributed masses m1 and m2, moving at angular velocities ω1 and ω2. the two objects are brought together edge to edge, ie they collide. obviously as a result of this collision, the objects' angular velocities change. in order for such a change to occur, a torque must be applied. what I don't know is, where is the torque coming from that initiates this change, and what is the equation that describes that torque? it's an entirely conceptual question.
Homework Equations
The usual suspects:
T = r x F (torque = cross product of object's position and the force)
ω = α t + ω0 (angular velocity = angular acceleration x time plus initial angular velocity)
beyond this, I'm not sure what other equations apply.
The Attempt at a Solution
it's conceptual, so I've mostly been muddling it out by deductive reasoning. if two objects are in contact, their circumferences are moving at velocities v1=ω1 R and v2=ω2 R. If these two velocities are equal and in opposite directions, like gears, then (based on real-life observation) they should exert no torque on one another.
if their velocities are not equal in this fashion, then some force is exerted by one object on the other, to adjust the other's velocity towards this equal velocity. theoretically, the force should be proportional to the difference between the current and target velocities. but since i have no idea where this force comes from, that's about where my reasoning came to a halt.