When a rigid body is constrained to rotate about a fixed axis, it is said to be in pure rotational motion. In this case, the body rotates about the axis with a constant angular velocity, and the equations of rotational motion can be simplified.
The angular velocity of the body is constant and is denoted by ω. The moment of inertia of the body about the axis of rotation is denoted by I. The torque acting on the body is zero since there is no external force causing a change in the angular velocity.
The equations of rotational motion for a rigid body constrained to rotate about a fixed axis are:
ω = Δθ / Δt
where ω is the angular velocity, Δθ is the angular displacement, and Δt is the time taken for the displacement.
K = 1/2 I ω^2
where K is the kinetic energy, I is the moment of inertia, and ω is the angular velocity.
L = I ω
where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
These equations show that the kinetic energy and angular momentum of the body are conserved in pure rotational motion since the angular velocity is constant and there is no external torque acting on the body.
In addition, the power output of a torque acting on the body can be calculated using the equation:
P = τ ω
where P is the power output, τ is the torque acting on the body, and ω is the angular velocity.
Overall, the motion of a rigid body constrained to rotate about a fixed axis is relatively simple, since the angular velocity is constant and the equations of rotational motion are simplified.

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