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Dimensional Formula of Torque. The dimensional formula of torque is given by, M 1 L 2 T-2. Where, M = Mass; L = Length; T = Time; Derivation. Torque (T) = Moment of Inertia × Angular Acceleration . . . . (1) Since, Moment of Inertia (M.O.I) = Radius of Gyration 2 × Mass. ∴ The dimensional formula of Moment of Inertia = M 1 L 2 T 0. . . (2)
Describe how the magnitude of a torque depends on the magnitude of the lever arm and the angle the force vector makes with the lever arm. Determine the sign (positive or negative) of a torque using the right-hand rule. Calculate individual torques about a common axis and sum them to find the net torque.
Torque has the dimension of force times distance, symbolically T −2 L 2 M and those fundamental dimensions are the same as that for energy or work.
Torque is a measure of the force that can cause an object to rotate about an axis. Torque is what causes angular acceleration in an object about an axis. Hence, torque can be defined as the rotational equivalent of linear force. Torque Formula. Mathematically torque is represented as. τ = Fr sin (θ) Where, r is the length of the lever arm.
The dimension of torque is ML 2 T -2. From the above equation, when \ ( \theta = 90^o, \tau =rF \). Therefore, torque is highest when the applied force is perpendicular to the lever arm. The static torque can be easily measured by using the formula. The dynamic torque is challenging to measure.
Let us examine which variables torque depends on by thinking about its units: τ = Iα = [kg ⋅ m2][rad s2] = [kg ⋅ m2 s2] = [N ⋅ m] The last equality in the above equation comes from definition of Newtons: F = ma = [kg ⋅ m / s2] ≡ [N]. So we find that torque will have units of force times length.
Learn about the dimensions of torque, its derivation, and the dimensional formula of torque. Understand the role of mass, length, and time in the dimensional formula.
The quantity \(\vec{r} \times \vec{F}\) is called the torque of a force around a point (the origin from which \(\vec r\) is calculated, typically a pivot point or center of rotation). It is denoted with the Greek letter \(\tau\), “tau”:
Torque is the measure of how much a force acting on an object causes that object to rotate, creating a tendency for the object to rotate about an axis, fulcrum, or pivot. Torque is most commonly classified as "twist", rotational force, or angular force to an object and applying it to a system changes the angular momentum of the system.
1) The first formula of torque describes torque as the moment of force and expresses it as the cross product of Force and Lever Arm Length (Torque T=r xF) 2) The second torque formula expresses torque as the time rate change of angular momentum. T = ΔL/ΔT.