The document discusses motion in a plane, covering key concepts such as vectors, their properties, and operations including addition, subtraction, and multiplication. It also reviews types of motion like projectile and uniform circular motion, detailing equations related to time of flight, maximum height, and velocity components. The analysis of motion in two dimensions is primarily conducted using vector principles.

1. Motion in a Plane
Physics Presentation

2. Introduction to Motion in a Plane
• Motion in a plane involves movement in two
dimensions, described using vectors.

3. Scalar and Vector Quantities
• Scalar: Only magnitude (e.g., speed, mass)
• Vector: Magnitude and direction (e.g.,
velocity, force)

4. Position and Displacement Vectors
• Position vector: Represents location relative to
origin.
• Displacement vector: Change in position.

5. General Vectors and Notations
• Vectors are represented using arrows.
Notations: , , etc.
A⃗ B⃗

6. Equality of Vectors
• Two vectors are equal if they have the same
magnitude and direction.

7. Multiplication of Vectors by a Real
Number
• Scaling a vector changes its magnitude but not
direction.

8. Addition and Subtraction of
Vectors
• Vectors are added using the triangle or
parallelogram law.

9. Unit Vector and Resolution of
Vectors
• Unit vector: Has magnitude 1.
• Resolution: Splitting a vector into
components.

10. Rectangular Components
• Any vector can be resolved into x and y
components.

11. Scalar and Vector Product of
Vectors
• Scalar (dot) product: A•B = AB cosθ
• Vector (cross) product: A×B = AB sinθ

12. Motion in a Plane
• Motion with two-dimensional displacement,
velocity, and acceleration.

13. Uniform Velocity and Acceleration
• Uniform velocity: Constant speed and
direction.
• Uniform acceleration: Constant rate of velocity
change.

14. Projectile Motion
• Motion under gravity with horizontal and
vertical components.

15. Uniform Circular Motion
• Motion along a circular path with constant
speed but changing velocity.

16. Conclusion
• Motion in a plane is analyzed using vectors,
equations, and motion principles.

17. Projectile Motion - Time of Flight
• T = (2u sinθ) / g

18. Projectile Motion - Maximum
Height
• H = (u² sin²θ) / (2g)

19. Projectile Motion - Horizontal
Range
• R = (u² sin2θ) / g

20. Projectile Motion - Velocity
Components
• Horizontal velocity: Vx = u cosθ
• Vertical velocity: Vy = u sinθ - gt
• Resultant velocity: V = √(Vx² + Vy²)

21. Uniform Circular Motion - Angular
Velocity
• ω = θ / t

22. Uniform Circular Motion - Linear
Velocity
• v = rω

23. Uniform Circular Motion -
Centripetal Acceleration
• aₐ = v² / r = ω² r

24. Uniform Circular Motion -
Centripetal Force
• Fₐ = m v² / r = m ω² r