Torque is the twisting force that tends to cause rotation.
Direction of Torque:
If the force causes counterclockwise rotation, the torque is positive.
If the force causes clockwise rotation, the torque is negative.
Units of Torque:
SI unit: Newton-meter (N·m)
CGS unit: Dyne-centimeter (dyne·cm)
Conditions for Equilibrium:
For an object to be in rotational equilibrium, the net torque acting on it must be zero.
This means that the sum of all clockwise torques must equal the sum of all counterclockwise torques.
Examples of Torque in Daily Life:
Opening a door by pushing the handle
Using a wrench to tighten a bolt
A seesaw balancing on a pivot
Turning the steering wheel
Buoyancy
Buoyancy is the upward force exerted by a fluid (liquid or gas) on an object placed in it. This force acts opposite to gravity and is responsible for objects floating or sinking in a fluid.
Fb = Buoyant force (N)
ρ = Density of the fluid (kg/m³)
g = Acceleration due to gravity (9.8 m/s²)
V = Volume of fluid displaced (m³)
Real-Life Applications of Buoyancy:
Ships and Boats: Designed to displace enough water to stay afloat.
Hot Air Balloons: Rise because the hot air inside is less dense than the surrounding air.
Submarines: Adjust their density using ballast tanks to float or sink.
Hydrometers: Measure liquid density based on how high they float.
Terminal Velocity
Terminal velocity is the maximum constant speed an object reaches when falling through a fluid (such as air or water). It occurs when the downward force of gravity is balanced by the upward force of air resistance (drag), meaning there is no net acceleration.
Forces Acting on a Falling Object:
Gravity (Weight, W)
Acts downward, pulling the object toward the Earth.
Given by W=mg, where mmm is mass and g is acceleration due to gravity (9.8 m/s²).
Air Resistance (Drag Force, Fd)
Acts upward, opposing the motion.
Increases with speed until it equals weight.
How Terminal Velocity is Reached:
When an object first starts falling, gravity dominates, and the object accelerates downward.
As speed increases, air resistance also increases.
Eventually, air resistance grows equal to the object's weight, and net force becomes zero.
At this point, the object stops accelerating and continues falling at a constant velocity—this is called terminal velocity.
vt = Terminal velocity (m/s)
m = Mass of the object (kg)
g = Acceleration due to gravity (9.8 m/s²)
ρ = Density of the fluid (kg/m³)
A = Cross-sectional area of the object (m²)
Cd = Drag coefficient (depends on shape and surface texture)
Factors Affecting Terminal Velocity:
Mass of the Object: Heavier objects generally have higher terminal velocity.
Shape and Surface Area: A larger surface area increases air resistance, reducing terminal velocity.
Density of the Fluid: Falling through air vs. water changes terminal velocity (it’s much lower in water).
Drag Coefficient: Streamlined objects (like skydivers in a head-first position) have lower drag and higher terminal velocity.
Examples:
Skydiving: A skydiver in a belly-down position has a terminal velocity of ~55 m/s (200 km/h), but in a head-down position, it can increase to ~90 m/s (324 km/h).
Raindrops: They fall at terminal velocity (~9 m/s) due to air resistance, preventing them from causing damage.
Parachutes: Increase air resistance dramatically, reducing terminal velocity and allowing safe landings.