⚡ Fast Revision: Force & Turning Effects
- Definition: The turning effect of a force about a fixed point or axis.
- Factors: Depends on the Magnitude of Force and the Perpendicular Distance from the pivot.
- Direction: Clockwise (taken as negative) or Anticlockwise (taken as positive).
Moment of Force: $\tau$ | SI Unit: Newton-metre (N m)
CGS Unit: dyne-cm | Conversion: $1\ N\ m = 10^7\ dyne\ cm$
Moment of Force = $F \times d$
($d$ = Perpendicular distance from the axis of rotation)
Applying force directly at the pivot/hinge. Fix: The moment of force is zero if the distance ($d$) is zero. Always apply force at the maximum distance to reduce effort.
⚡ Fast Revision: Pressure in Solids
- Thrust: The total force acting normally (perpendicularly) on a surface.
- Pressure: Thrust acting per unit area of a surface.
- Relationship: Pressure is inversely proportional to the area of contact.
Pressure: P | SI Unit: Pascal (Pa) or $N/m^2$
Thrust SI Unit: Newton (N)
$P = \frac{Thrust (F)}{Area (A)}$
| Application | Area Adjustment | Resulting Pressure |
|---|---|---|
| Sharp Knife / Nails | Small Area | High Pressure (Easy cutting) |
| Foundation of Building | Wide Area | Low Pressure (Prevents sinking) |
| School Bag Straps | Wide Area | Low Pressure (Comfortable) |
Forgetting to convert Area to $m^2$. Fix: If area is in $cm^2$, divide by 10,000 to get $m^2$ before calculating Pascal.
⚡ Fast Revision: Pressure in Fluids (Liquids)
- Transmission: Liquids exert pressure in all directions (sideways, upwards, and downwards).
- Depth: Pressure increases linearly with the depth from the free surface.
- Density: Pressure is directly proportional to the density of the liquid.
$P = h \times \rho \times g$
($h$ = depth, $\rho$ = density, $g$ = acceleration due to gravity)
Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the vessel.
| Point of Interest | Pressure Status |
|---|---|
| Same Horizontal Level | Pressure is equal at all points. |
| Bottom of the Dam | Maximum Pressure (Why walls are thicker at the base). |
| Shape of Vessel | Does NOT affect liquid pressure. |
Confusing "Height" with "Depth". Fix: In $P = h\rho g$, '$h$' is the vertical distance downward from the top surface, not the height from the bottom.
⚡ Fast Revision: Atmospheric Pressure
- Definition: The thrust exerted per unit area on the earth's surface by the column of air above it.
- Variation: It decreases as we go higher above sea level (air becomes less dense).
- Standard Value: At sea level, it is about 1.013 $\times$ 10⁵ Pa (or 76 cm of Mercury).
Barometer: Instrument used to measure atmospheric pressure.
Common Units: bar, millibar, torr, and atm.
| Phenomenon | Reasoning |
|---|---|
| Nose Bleeding at Altitudes | Blood pressure becomes higher than low external atmospheric pressure. |
| Sucking juice with straw | Air pressure inside straw drops; external atmosphere pushes liquid up. |
| Rubber Sucker | Air is kicked out, atmospheric pressure holds it firmly to the surface. |
Thinking we are crushed by atmospheric pressure. Fix: Our internal blood pressure is slightly higher than atmospheric pressure, balancing the force.