UNIFORM CIRCULAR MOTION

🔹 What is Circular Motion?

• Movement of an object along a circular path.

• Uniform Circular Motion: Motion at constant speed along a circular path.

🔹 Examples of Circular Motion:

• Artificial satellite orbiting Earth

• Stone tied to a rope being swung in a circle

• Car turning a corner on a racetrack

• Electron moving in a magnetic field

• Gears rotating in a machine

📐 ANGULAR DISPLACEMENT & ANGULAR VELOCITY

🔹 Angular Displacement

• The angle (in radians) through which an object moves on a circular path.

• Not linear; it’s about rotation.

🔹 Angular Velocity (ω)

• Rate of change of angular displacement.

• Formula: ω = θ / t
  (θ = angular displacement, t = time)

🔹 Measurement Units:

• Revolutions: 1 full turn = 360°

• Degrees: Angle measurement

• Radians: 1 revolution = 2π rad, so
  180° = π rad

🔹 Relationship:

• θ = s / r
  (θ = angular displacement, s = arc length, r = radius)

🧭 TANGENTIAL (LINEAR) VELOCITY & ANGULAR VELOCITY

🔹 Tangential Velocity (v)

• Direction is always along a tangent to the circle.

• Speed remains constant, direction changes → velocity changes.

🔹 Relationship:

• v = ω × r

🔹 Summary: anything that moves in circular path:

• Moves with steady speed

• Changes direction constantly

• Accelerates towards the center (even if speed is constant)

• Object never gets closer to the center

🎯 CENTRIPETAL FORCE

🔹 Definition:

• Force directed towards the center of the circle.

• Keeps object in circular motion.

🔹 Examples:

1. Car turning → friction between tyres and road

2. Whirling ball on string → tension in string

3. Earth orbiting Sun → gravity provides the force

🔹 More Centripetal Force is Needed When:

• Object’s mass increases

• Speed increases

• Radius decreases

🔹 Centripetal Acceleration (ac):

• ac = v² / r

🔹 Centripetal Force (Fc):

• Fc = mv² / r

⚙️ APPLICATIONS OF UNIFORM CIRCULAR MOTION

1. Car Negotiating a Corner

• Two forces act:
  • Normal force (N): Balances the car’s weight

  • Friction (Fs): Provides the centripetal force

• Fc = Fs

2. Car on a Banked Road

• Banking angle helps provide Fc without relying on friction

• Smoother, safer turning at high speeds

3. Aircraft Banking

• Pilot tilts wings

• Vertical lift = balances weight

• Horizontal lift = provides Fc

4. Planets in Orbit

• Fc is provided by gravitational pull

• Move in uniform circular paths

5. Roads and Cornering

• Roads are banked to improve stability

• Prevent skidding and accidents

6. Spin Dryer (Washing Machine)

• Clothes press against drum wall

• Water forced out due to high-speed spinning

• Centripetal motion helps dry clothes

7. Centrifuge

• Separates liquids by spinning

• Denser substances move outward

• Used in:
  • Food processing (e.g. oil separation)

  • Medical labs

  • Astronaut training for high G-forces