Formula to calculate force as a function of angle

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To calculate the force required to push a rotating arm attached to a shaft, the formula must account for the torque at the shaft, which is 1 Nm, and the geometry of the system. The sliding arm's perpendicular contact at 0 degrees creates a leverage effect, with the distance from the shaft's center to the contact point being 3 cm. As the shaft rotates from -45 to +45 degrees, the force will vary based on the angle due to the changing moment arm. A hyperbolic function may model this relationship, adjusted for the rotating arm's width of 1 cm. A diagram would greatly aid in visualizing the mechanics involved in this calculation.
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What formula can I use to calculate the force I need to apply to a sliding arm that makes a point contact along the edge of a rotating arm attached to a shaft driving a load in order to push the rotating arm to rotate the shaft? The rotating arm is 1 cm wide. The load at the shaft is 1 Nm torque. The shaft rotates from -45 through +45 degrees. The sliding arm is perpendicular to the edge of the rotating arm when the shaft is at 0 degrees. At that angle, the distance between the center of the shaft and the point along the center line of the rotating arm closest to the point of contact between the two arms is 3 cm. I would like to calculate force as a function of the angle of the shaft. I imagine it is some type of hyperbolic function offset by ½ the width of the rotating arm. Thanks!
 
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A diagram is needed.
 

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