Rotation Work Equation: Torque x Displacement = Rotational Equivalent

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The rotational equivalent of the work equation is expressed as work = torque * angle. Torque replaces force, while angle, measured in radians, serves as the displacement in rotational contexts. Torque has the same dimensions as work, meaning it can be expressed in Joules or Newton-meters. The relationship indicates that displacement in rotational problems is the product of radius and angle, while torque is defined as force multiplied by radius. This formulation clarifies how rotational mechanics parallels linear work equations.
24forChromium
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what would be the rotational equivalent of:

work = force * displacement

?

I assume that the force should be replaced with torque, but have no idea what the displacement should be replaced with, angles in radian? I'd appreciate it to see some units too.
 
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24forChromium said:
angles in radian?
Yes
 
A.T. said:
Yes
any ideas what the rest of the equation and its units look like?
 
24forChromium said:
any ideas what the rest of the equation and its units look like?
As A.T has pointed out, your first post has the complete answer: work = torque * angle
where torque has the same dimensions as work (i.e energy) given that angles are dimensionless. Units of torque: Joules or equivalently Newton * meters. Units of angle: radians.
 
The point is for rotational problems, your displacement is the radius * angle and force * radius is precisely the torque acting on a particle.
 
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