A dynamic quantity {momentum}| depends on mass and velocity. Momentum p equals mass m times velocity v: p = m*v. Constant force F times time change (tf - ti) makes momentum p: p = F * (tf - ti) = m * a * (tf - ti) = m*v. Force F is momentum change dp per time change dt: F = dp / dt.
Momentum {angular momentum}| can be through angles around rotation axes or points. Momentum p equals mass m times velocity v: p = m*v. Tangential momentum pt equals mass m times tangential velocity vt, which equals angular velocity w times circle curvature radius r: pt = m * vt = m*w*r. Angular momentum L equals tangential momentum pt times radius r: L = pt * r.
Moment of inertia I equals mass m times radius r squared: I = m * r^2. Angular momentum L equals moment of inertia I times angular velocity w: L = pt * r = (m*w*r) * r = (m * r^2) * w = I*w.
torque
Force F equals mass m times acceleration a: F = m * a. Tangential force Ft equals mass m times tangential acceleration at: Ft = m * at = m * dv / dt = m * r * dw / dt, where dv is velocity change, dt is time change, dw is angular-velocity change, and r is curvature radius. Torque T equals tangential force Ft times radius r: T = Ft * r = (m * at) * r = m * r * (dw / dt) * r = (m * r^2) * dw / dt = I * (dw / dt) = I * aa, where m is mass, at is tangential acceleration, r is curvature radius, dw is angular-velocity change, dt is time change, I is moment of inertia I, and aa is angular acceleration.
Force F equals momentum change dp over time change dt: F = dp / dt. Tangential force Ft equals tangential momentum change dp over time change dt: Ft = dp / dt = m * r * dw / dt, where m is mass, r is curvature radius, dw is angular-velocity change, and dt is time change. Torque T equals angular momentum change dL over time change dt: T = dL / dt = (m * r^2) * dw / dt, where m is mass, r is curvature radius, and dw is angular-velocity change.
Force acts over time {impulse}|, to change object motion.
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Date Modified: 2022.0225