Physics Unit 4 Forces: Vectors and Moments Notes

Equilibrium: For a system to be in equilibrium, there should be no resultant force and resultant torque acting on the system.

The triangle of forces is a closed triangle drawn for an object in equilibrium. The sides of the triangle represent the forces in both magnitude and direction.

If the vector makes an angle theta with the horizontal side, then:

·       Fhor = F cos theta

·       Fver = F sin theta

 

A free-body diagram represents all forces acting on 1 object.

Cos (90 – theta) = Sin theta

Moment of Force: The moment of force is calculated about a point. It is the product of the force and the perpendicular distance between the line of action of the force and the point.

Moment = F2 x d x sin theta

Couple: A pair of equal and opposite forces that act on an object at different points and produce rotation only.

Torque: The product of one of the forces and the perpendicular distance between the forces.

Note:- An object experiencing torque is not in equilibrium, because there is a resultant turning effect.

 

Contact force:

1.       If a beam is fixed to a wall at one end, and no other forces are acting on it. Then the beam is in equilibrium. The weight of the beam is balanced by the upward contact force at the wall.

2.       If a ladder is resting such that its base is on the ground (rough surface) and the top is leaning against a smooth wall. Since there is less friction between the top of the ladder and the smooth wall, the ladder would rotate around the contact point between them.

3.       Suppose a wheel is supported by a pin at its centre of gravity, then the weight of the wheel is balanced by the contact force at the pin.