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 General Physics General Physics Help Forum Jul 12th 2017, 05:10 PM #1 Junior Member   Join Date: Feb 2017 Posts: 7 equation of motion Could someone explain equation 2? (the part with the red frame) Thank you   Jul 13th 2017, 04:40 AM #2 Senior Member   Join Date: Aug 2008 Posts: 113 $\tau_{net} = J_0 \alpha = Tr + F_s R$ Hooke's law for an ideal linear spring says ... $F_s = -kx$ recall arc length equals radius times angular displacement ... $x = R \cdot \Delta \theta$ $R = 4r$ and $\Delta \theta = \theta_0 + \theta$, where $\theta_0$ is the angular displacement of the pulley at system equilibrium, and $\theta$ is the additional angular displacement beyond equilibrium to induce an oscillation of the system. $F_s R = -k \color{blue}{x} \cdot \color{red}{R} = -k \cdot \color{blue}{4r(\theta_0+\theta)} \cdot \color{red}{4r}$ Last edited by skeeter; Jul 13th 2017 at 06:36 AM.   Jul 13th 2017, 06:22 AM #3 Junior Member   Join Date: Feb 2017 Posts: 7 Thank you very much. Does the second 4r refer to θ?   Jul 13th 2017, 06:35 AM   #4
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Join Date: Aug 2008
Posts: 113
 Thank you very much. Does the second 4r refer to θ?
The second $4r$ is the radius in the torque formula. The first $4r$ is used to calculate the arc length, $x$.

Check my last post again ... I color-coded it.

Last edited by skeeter; Jul 13th 2017 at 06:37 AM.  Tags equation, motion Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post StudyMadeEasy Kinematics and Dynamics 3 Feb 21st 2017 01:57 PM petdem Thermodynamics and Fluid Mechanics 8 Feb 15th 2010 05:51 AM bonnie.huang Kinematics and Dynamics 1 Jul 7th 2009 03:57 AM ipinkbaby Kinematics and Dynamics 1 Jun 14th 2009 12:31 AM asi123 Quantum Physics 2 May 29th 2009 04:23 AM