Thus we get Torque = T = moment of force = product of lever arm length and the force component causing rotation = r F sinθ = r x F ………………(a) Here, ‘X’ denotes Cross Product of vectors. Rather, the effective force that generates torque = Vertically resolved component of F = F sinθ. Because this is the component that causes rotation in this case.ĭ4: See how F Sin(Theta) component causes rotation Thus we get Torque = r F sin(Theta) = r X Fįrom the above diagram, we can see that as the F (in red arrow) is applied at an angle theta with the lever arm(in yellow), the entire force F can’t act to create the rotation. – If the force is applied perpendicular to the radius of rotation then the entire force F is responsible for the rotation – But if the force is not perpendicular, the perpendicular component of the force must be found. – The lever arm is the perpendicular distance from the axis of rotation to the point where the force is exerted. – When a Force is applied on a particle and that particle starts to rotate or tends to rotate about an axis then it is generally said that a Moment of force is generated. This derivation of the T formula is based on our understanding of Torque as the Moment of force. Derive formula of torque as the cross product of force and lever arm length. The third Formula for torque: Torque is also expressed as the cross product of Moment of Inertia(I) and Angular Acceleration( α) T= I X α ……………(3) (Tao = I cross Alpha) here, I stands for Moment of inertia and α is the angular acceleration Derivation of Torque formulaĭerivation of torque formula is done here in 3 different ways and shown in detail in the next 3 sections. Torque Formula in terms of Moment of Inertia(I) and Angular Acceleration( α) T = ΔL/ΔT …………(2) Here ΔL is the change in angular momentum and ΔT is the time duration when this change happens. The second formula of Torque: Torque can also be defined as the time rate of change of angular momentum. Formula of Torque in terms of rate of change of angular momentum F Sin θ is the perpendicular component of the force which is the actual component of the applied force responsible for the rotation. T = r x F = r F Sin θ ………….(1) Lever arm length r is the shortest distance between the rotation axis and the point of application of the force and θ = angle made between Lever arm and the line of action of the force being applied. It is the cross product of Lever Arm Length (r) and the Force applied (F). Torque formula can be framed considering Torque as the Moment of Force. Formula of Torque in terms of Lever Arm Length (r) and the Force applied (F) The torque formula is presented here in 3 different forms and those are (1) torque as the moment of force (2) Torque as the time rate change of angular momentum, and (3) Torque as the time rate change of angular momentum. 3 different forms of Torque formula in physics This post is apt for students of class 11 and 12 (CBSE, ICSE and other international boards as well). And then we will derive all three equations one by one. In the next sections, we will write three equations or formulas of torque again with a short description for each. Torque is the Moment of Force (Rotational domain equivalent of Force) which is the determining factor of how effectively a force can twist or turn something.
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