2026-08-19 19:01:21: Rotational Inertia

physics/Torque and Rotational Dynamics/Connecting Linear and Rotational Motion.md

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+[[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: $$s=r\theta$$

physics/Torque and Rotational Dynamics/Rotational Inertia.md

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+[[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:
+$$I_{tot}=\Sigma I_i=\Sigma m_i r^2$$
+

physics/Torque and Rotational Dynamics/Rotational Kinematics.md

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+[[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. 
+$w=w_0+at$
+$\theta=\theta_0+w_0t+\frac{1}{2}at^2$
+$w^2=w^2_0+2a(\theta - \theta_0)$
+

physics/Torque and Rotational Dynamics/Torque and Rotational Dynamics.md

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+[[physics]]

physics/Torque and Rotational Dynamics/Torque.md

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+[[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.
+