The Total Torque calculator computes the total torque of a rotating body based on the angular acceleration and the mass moment of inertia.
INSTRUCTIONS: Choose units and enter the following.
Total Torque (τ): The torque is returned in Newton-meters (N•m). However this can be automatically converted to compatible units via the pull-down menu.
The total torque, τ , of a rotating body is related to the body's moment of inertia and angular acceleration. The formula for total torque is:
where:
The moment of inertia, I, is the property of a rigid mass that defines the torque required to cause angular acceleration of the body about a fixed axis of rotation. In the picture, the z-axis is a fixed axis of rotation about which the mass is rotating.
The moment of inertia, I, varies with the shape of the mass and also varies with the axes of rotation. in the picture, the small component mass, a small piece of the rotating body, is shown rotating about the axis of rotation, z. The each component element of the body as as whole experiences force as it rotations about the z-axis. That force on the component mass, m, can be represented as a radial and a tangential force component. Only the tangential component of force contributes to the toque required to cause the mass to rotate.
An increase in moment of inertia around an axis corresponds to increased torque required to change the rotation rate of the mass.
The moment of inertia is directly dependent on the distribution of mass and can be integrated from the sum of the moments of inertia of component masses making up the whole mass.
`tau_"total" = I * alpha`