Translational and Rotational motion Lever arm or moment arm Top view or a door. In above Figure, if you apply a force `F_A` to the door as shown, you will find that the greater the magnitude , `F_A`, the more quickly the door opens. But now if you apply the same magnitude force at a point closer to the hinge,`F_B`, the door will not open so quickly. We find the angular acceleration of the door is proportional not on only to the magnitude of the force, but is also directly proportional to if `r_A = 3r_B` than `α_A = 3α_B` In other word, `F_B` must be three times as large as `F_A` to give the same angular acceleration. Torque The angular acceleration is proportional to the product of the force times the lever arm. This product is called the moment of the force about the axis, or ,more commonly it is called the torque (`τ`) If the force applied is not perpendicular with the arm, can find the perpendicular lever arm `r_⊥ = r sinθ` as shown in figure (a) `τ = r sinθ F` of we can find the perpendicular component of the applied force `F_⊥ = Fsinθ` as shown in figure (b) `τ = r Fsinθ `