Turning Effect of Forces

Parallel Forces: Forces acting parallel to each other.
Types:

• Like Parallel Forces: Forces acting in the same direction (e.g., weight of apples in a bag).
• Unlike Parallel Forces: Forces acting in opposite directions (e.g., forces on a see-saw).

Head-to-Tail Rule: A graphical method to add vectors. Draw the first vector; draw the second vector starting from the head of the first. The resultant vector ($R$) is drawn from the tail of the first to the head of the last vector.

Splitting a force into two mutually perpendicular components is called resolution of force.
Horizontal Component: $F_x = F \cos \theta$
Vertical Component: $F_y = F \sin \theta$

If $F_x$ and $F_y$ are known, the force $F$ can be found:
Magnitude: $F = \sqrt{F_x^2 + F_y^2}$
Direction: $\theta = \tan^{-1} \frac{F_y}{F_x}$

Torque ($\tau$): The turning effect of a force.
Formula: $\tau = F \times L$ (force $\times$ moment arm).
Unit: Newton-metre ($Nm$).
Moment Arm ($L$): The perpendicular distance from the axis of rotation to the line of action of the force.

A body is balanced if the sum of clockwise moments is equal to the sum of anticlockwise moments acting on it.

A couple is formed by two unlike parallel forces of the same magnitude but not along the same line.
Example: Forces on a steering wheel.

Centre of Mass: The point where an applied force causes the system to move without rotation.

Centre of Gravity: The point where the whole weight of the body appears to act vertically downward.
The C.G. of uniform shapes lies at their geometric centers.

The C.G. of an irregular lamina can be found using a Plumbline. When suspended freely, the C.G. always lies vertically below the point of suspension.

Equilibrium: A body is in equilibrium if no net force acts on it (it remains at rest or moves with uniform velocity).

• First Condition: Vector sum of all forces is zero ($\Sigma F = 0$).
  $\Sigma F_x = 0$, $\Sigma F_y = 0$.
• Second Condition: Vector sum of all torques is zero ($\Sigma \tau = 0$). Needed because 1st condition doesn't guarantee no rotation (e.g., couple).

1. Stable Equilibrium: If a body returns to its original position after a slight tilt (C.G. rises).
2. Unstable Equilibrium: If a body moves further away from its original position after a slight tilt (C.G. lowers).
3. Neutral Equilibrium: If a body stays in its new position after being disturbed (C.G. height remains same).

Stability can be improved by:
1. Lowering the Centre of Gravity.
2. Increasing the area of the base.
Example: Racing cars have low height and wide base.