A mirror on side pivots experiences a turning moment when its center of mass lies to one side of the pivot. Calculate that gravity moment from mirror mass and the horizontal offset, then compare it with a known resisting moment.
Mirror Pivot Gravity-Moment Calculator
Enter mirror mass, signed horizontal center-of-mass offset and an independently known resisting moment. The worksheet performs a static moment comparison only; it does not design or rate a friction pivot.
Equation Used
- Gravity is 9.80665 m/s2 and the mirror is treated as a rigid body.
- The entered horizontal offset is measured in the current pose.
- The resisting moment is independently known for that exact joint and condition.
- Bearing friction, preload relaxation, wear, impact, adjustment force, frame compliance and safety factors are excluded.
Weight multiplied by the horizontal distance from the pivot to the center-of-mass line gives the gravity moment. The result describes the current pose, not the capacity of the joint.
Cheval frame, horizontal pivot and gravity moment
A cheval mirror rotates about side pivots carried by a floor stand. Weight acts vertically through the assembly center of mass. Its turning effect about the pivot is weight multiplied by the perpendicular distance to that vertical line of action.
The schematic shows the signed horizontal offset between the pivot and the vertical line of action of weight.
Comparing static moments
Use the calculator to find the gravity moment for a measured pose and compare it with an independently characterized resisting moment. It does not specify hardware, preload or safe stability.
Moment about the pivot
This is the planar cross-product result for a vertical force. If the center-of-mass line passes through the pivot, x and the gravity moment are zero.
Static-moment example
An 8 kg assembly has weight 78.45 N. With its center-of-mass line 20 mm to the positive side of the pivot, signed gravity moment is +1.57 N m. Against an entered 4.00 N m resistance, the arithmetic residual is 2.43 N m.
Gravity moment and friction capacity
MIT statics defines moment by the perpendicular distance to the force line. Real friction capacity varies with joint construction, clamp load, materials, contamination, wear and motion history, so no universal hold claim is made.
Mirror-pivot questions
What does a negative offset mean?
The center-of-mass line is on the opposite side of the selected positive direction, so moment sign reverses.
Does positive residual guarantee no drift?
No. It is only a comparison with the entered resisting moment.
Does the worksheet check stand tip-over?
No.
Statics references
- MIT OpenCourseWare, Static Equilibrium Force and Moment: moment magnitude as force times perpendicular distance and the vector cross-product definition.
- NASA Glenn, Torque (Moment): torque about a pivot as force times perpendicular distance.
- NASA, Weight and Balance Lesson 2: center of gravity, moment arm and balance context.
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