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Perfectly inelastic collisions: -$$v_f=\frac{m_1v_1+m_2v_2}{m_1m_2}$$ +$$v_f=\frac{m_1v_1+m_2v_2}{m_1+m_2}$$ ![[Pasted image 20260819112153.png]] # Elastic Collision Energy Conservation Formula $$\frac{1}{2}m_1v^2_{1i}+\frac{1}{2}m_2v^2_{2i}=\frac{1}{2}m_1v^2_{1f}+\frac{1}{2}m_2v^2_{2f}$$ diff --git a/physics/Torque and Rotational Dynamics/Connecting Linear and Rotational Motion.md b/physics/Torque and Rotational Dynamics/Connecting Linear and Rotational Motion.md new file mode 100644 index 0000000..9a6f1fb --- /dev/null +++ b/physics/Torque and Rotational Dynamics/Connecting Linear and Rotational Motion.md @@ -0,0 +1,6 @@ +[[Torque and Rotational Dynamics]] + +# Summary +* Linear velocity related to angular velocity: $$v=rw$$ v= velocity r=how far w=angular velocity +* Tangential acceleration relates to linear acceleration: $$A_T=ra$$ +* Arc length and angle linked by: $$s=r\theta$$ \ No newline at end of file diff --git a/physics/Torque and Rotational Dynamics/Rotational Inertia.md b/physics/Torque and Rotational Dynamics/Rotational Inertia.md new file mode 100644 index 0000000..e195dd7 --- /dev/null +++ b/physics/Torque and Rotational Dynamics/Rotational Inertia.md @@ -0,0 +1,9 @@ +[[Torque and Rotational Dynamics]] +For a point mass:$$I=mr^2$$ +$I$ is rotational inertia (kg * $m^2$) +m is mass +r is radial distance + +Several discrete objects: +$$I_{tot}=\Sigma I_i=\Sigma m_i r^2$$ + diff --git a/physics/Torque and Rotational Dynamics/Rotational Kinematics.md b/physics/Torque and Rotational Dynamics/Rotational Kinematics.md new file mode 100644 index 0000000..c8143f7 --- /dev/null +++ b/physics/Torque and Rotational Dynamics/Rotational Kinematics.md @@ -0,0 +1,18 @@ +[[Torque and Rotational Dynamics]] + +# Summary +* Angular displacement is measured with $\Delta \theta=\theta-\theta_0$ +* Track angular displacement direction with clockwise counterclockwise sign convention +* Average angular velocity: $w_{avg}=\frac{\Delta\theta}{\Delta t}$ +* Average angular acceleration: $a_{avg}=\frac{\Delta w}{\Delta t}$ +* Rigid system holds shape, but different parts move at different speeds so you can't treat it as a single particle unless COM motion describes rotation well +* Slope of theta vs time shows angular velocity +* Slope of angular velocity vs time shows angular acceleration +* Integral of angular velocity vs time shows Delta theta + +# Angular vs. Linear Motion +Angular motion equations are similar to linear motion equations. +$w=w_0+at$ +$\theta=\theta_0+w_0t+\frac{1}{2}at^2$ +$w^2=w^2_0+2a(\theta - \theta_0)$ + diff --git a/physics/Torque and Rotational Dynamics/Torque and Rotational Dynamics.md b/physics/Torque and Rotational Dynamics/Torque and Rotational Dynamics.md new file mode 100644 index 0000000..5547faf --- /dev/null +++ b/physics/Torque and Rotational Dynamics/Torque and Rotational Dynamics.md @@ -0,0 +1 @@ +[[physics]] \ No newline at end of file diff --git a/physics/Torque and Rotational Dynamics/Torque.md b/physics/Torque and Rotational Dynamics/Torque.md new file mode 100644 index 0000000..0ef25e3 --- /dev/null +++ b/physics/Torque and Rotational Dynamics/Torque.md @@ -0,0 +1,10 @@ +[[Torque and Rotational Dynamics]] + +Twisting effect a force has around an axis of rotation. + +# Summary +* Only the force component perpendicular to $\vec r$ generates torque. +* Magnitude of torque: $$\tau=rF\sin \theta=rF_\perp$$ +* Torque is at its largest when the force is applied 90$\degree$ to r. +* Force diagrams are like FBD but shows how each force acts relative to the axis. +