bolzano95
- 89
- 7
- Homework Statement
- Write a differential equation for a mass-spring system.
- Relevant Equations
- F=ma
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The discussion focuses on solving a mass-spring system influenced by torque in a pulley, specifically addressing the confusion surrounding the definitions of torque and moment of inertia. Participants clarify that a frictionless pulley implies no friction at the axle, not between the rope and pulley. The correct relationship is established as torque (τ) equaling moment of inertia (I) multiplied by angular acceleration (α), with the equation τ = Iα being central to the analysis. The conversation emphasizes the importance of correctly interpreting the problem statement and ensuring all necessary terms are included in the equations.
PREREQUISITESStudents and professionals in physics, mechanical engineering, and applied mathematics who are working on problems involving rotational dynamics and mass-spring systems.
You don't mean that. A frictionless pulley means there is no friction at the axle.bolzano95 said:There is no friction between the rope and pulley.
Sorry, I meant the rope does not slip on the pulley.haruspex said:You don't mean that. A frictionless pulley means there is no friction at the axle.
If there were no friction between pulley and rope the pulley would not turn; the rope would just slide over it.
A few mistakes towards the end.
Torque = moment of inertia times.. what?
A factor of R seems to have disappeared somewhere.
Torque has dimension ##ML^2T^{-2}##. Moment of inertia is ##ML^2## and angular velocity is ##T^{-1}##. Multiplying those last two gives ##ML^2T^{-1}##, not torque.bolzano95 said:The torque in this case is given as a product of C and angular velocity
There is no damping here (much less dampening - all is dry). The forces are all conservative.bolzano95 said:C is a factor of dampening.
Either you were given the wrong formula or you have misunderstood.bolzano95 said:I have to use the given formula (it's mandatory)
Good point.Lnewqban said:The statement “... there is a torque in the axis or rotation” suggests to me that the shown diagram does not correspond with the text of this problem.