Torque acting on a rotating wedge due to a linear force parallel to the axis of rotation

Question

Let's say I have a wedge which can only be rotated about a fixed axis perpendicular to the ground. There is a cam follower mechanism constrained to vertical movement with a ball roller on the end which is applying a vertical force on this wedge at a fixed distance L from the center of rotation. As a function of F, theta, and L, how do I find the resultant torque? This is not schoolwork, it's based on a nutating mechanism I'm designing for my job.

kamran · Accepted Answer

Lets callthe cam force as per your sketch P. P will have 2 components acting on the surface of the wedge, $$P* cos(theta)_ text{paralel to surface} ,  P sin(theta)_ text{perpendicular to surface} $$
Bur both of these components pass through the center of rotation, meaning they will not produce any torque, hence any rotation.
If P is too big, the shaft at the center can bend or break but wont rotate.
EDIT
After you modified your question. And if we disregard the original sketch.
there is a varying lateral force that varies as the cam moves around.
This force F multiplied by L is your torque.
,  $F= Psin(theta)*sin(alpha)  , $ Sin of the local slope angle.
That angle Alph is a simple sine function, I let you figure it.

Torque acting on a rotating wedge due to a linear force parallel to the axis of rotation

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