Applied Mechanics and Graphic Statics
A body of weight ‘w’ placed on an inclined plane is acted upon by a force ‘P’ parallel to the plane which causes the body just to move up the plane. If the angle of inclination of the plane is ‘θ’ and angle of friction is ‘φ’, the minimum value of ‘P’, is

w sinθ cos(θ - φ)/sin φ
w sin (φ - θ)/cos φ
w cos (θ + φ)/cos φ
w sin (θ - φ)/cos φ

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Applied Mechanics and Graphic Statics
Newton’s Law of Motion is:

The rate of change of momentum is directly proportional to the impressed force, and takes place in the same direction, in which the force acts
Everybody continues in its state of rest or of uniform motion in a straight line, unless it is acted upon by some external force
To every action, there is always an equal and opposite reaction
All listed here

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Applied Mechanics and Graphic Statics
A square hole is punched out of a circular lamina, the diagonal of the square being the radius of the circle. If ‘r’ is the radius of the circle, the C.G. of the remainder from the corner of the square on the circumference will be

[r (π - 0.25)]/(π - 0.5)
[r (π + 0.25)]/(π + 0.5)
[r (π - 0.5)]/(π + 0.25)
[r (π + 0.25)]/(π - 0.5)

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