Forces {torque}| can tend to cause motions around rotation centers.
acceleration
Torque causes angular acceleration. For example, force can act on a rigid rod that can turn around a balance point. Force can act perpendicular to rod or at another angle. Torque T is force F times radius r from balance point times sine of force-to-radius angle A: T = F * r * sin(A), which is cross product of force and radius vectors: T = F X r. Torque-vector direction is perpendicular to both force vector and radius vector and parallel to axis.
moment of inertia
Tangential force Ft equals mass m times tangential acceleration at, which equals angular acceleration aa times radius r: Ft = m * at = aa * r. If torque acts perpendicular to radius, torque T equals moment of inertia (I = m*r^2) times angular acceleration aa: T = Ft * r = m * at * r = m * aa * r * r = m * (r^2) * aa = I * aa.
examples
Frisbees and yo-yos have torques. Torque causes car front to fall when car stops. Torque causes car front to rise when car accelerates. To open door, push farthest from hinge to apply least force, because radius is greatest. Spins in ice-skating begin with torque. Gymnasts and divers apply torque. Torque causes spin on footballs, bullets, bicycle wheels, helicopter blades, and propellers. Scales use opposing torques to weigh objects.
equilibrium
When lever is not moving around balance point {equilibrium}, right Tr and left Tl side torques, F * r * sin(A), are equal: Tl = F1l * r1l * sin(A1l) + F2l * r2l * sin(A2l) + ... = F1r * r1r * sin(A1r) + F2r * r2r * sin(A2r) + ... = Tr.
Physical Sciences>Physics>Dynamics>Rotation
Outline of Knowledge Database Home Page
Description of Outline of Knowledge Database
Date Modified: 2022.0224