Formula to calculate force as a function of angle

In summary, the conversation discusses the calculation of the force required to push a rotating arm attached to a shaft with a load. The rotating arm is 1 cm wide and the load is 1 Nm torque. The shaft rotates from -45 to +45 degrees, with the sliding arm perpendicular to the edge of the rotating arm at 0 degrees. The distance between the center of the shaft and the point of contact between the two arms is 3 cm at 0 degrees. The speaker is looking for a formula to calculate the force as a function of the shaft angle, which may involve a hyperbolic function offset by ½ the width of the rotating arm. A diagram is necessary for further understanding.
  • #1
PM22
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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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  • #2
A diagram is needed.
 

1. What is the formula to calculate force as a function of angle?

The formula to calculate force as a function of angle is F = mgsinθ, where F is the force, m is the mass of the object, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of inclination.

2. How is the formula derived?

The formula is derived from the basic principles of physics, specifically Newton's Second Law of Motion which states that force is equal to mass times acceleration. In this case, the acceleration is the component of the force acting in the direction of the angle of inclination.

3. Is this formula applicable to all objects?

Yes, this formula is applicable to all objects regardless of their mass, as long as they are subject to a force acting at an angle of inclination.

4. Can this formula be used to calculate force in a two-dimensional plane?

Yes, this formula can be used to calculate force in a two-dimensional plane, as long as the angle of inclination is measured from the horizontal plane.

5. Are there any limitations to this formula?

One limitation of this formula is that it assumes a frictionless and idealized environment. In real-life scenarios, other factors such as air resistance and friction may also affect the calculation of force as a function of angle.

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