Physics Mechanics: Kinematics and Forces Principles

Kinematics: Understanding Motion

Scalars and Vectors in Motion

• Scalars: Quantities possessing magnitude only (e.g., speed, distance, time, mass).

• Vectors: Quantities possessing both magnitude and direction (e.g., velocity, displacement, acceleration, force). These are represented by arrows.

  • Position: Displacement (Vector)

  • Change: Distance (Scalar), Displacement (Vector)

  • Rate: Speed (Scalar), Velocity (Vector)

  • Change in Rate: Acceleration (Vector)

Constant Acceleration Equations

• Variables Used: Final velocity (v), Initial velocity (u), Acceleration (a), Displacement (s), Time (t).

• Key Equations:

  • v = u + at

  • v² = u² + 2as

  • s = &frac12(u+v)t

  • s = ut + &frac12at²

  • s = vt - &frac12at²

Graphing Motion Characteristics

• Displacement-Time (s-t) Graph:

  • A flat line indicates the object is stationary.

  • The gradient represents the velocity.

• Velocity-Time (v-t) Graph:

  • A flat line signifies constant velocity.

  • The gradient represents the acceleration.

  • The area under the graph represents the displacement.

• Acceleration-Time (a-t) Graph:

  • A flat line shows constant acceleration.

  • The area under the graph represents the change in velocity.

Forces and Motion Dynamics

Newton's Laws of Motion

• First Law: An object's velocity remains constant unless acted upon by a net external force.

• Second Law: The net force equals mass times acceleration (F_net = ma).

• Third Law: For every action, there is an equal and opposite reaction (F_{on A by B} = -F_{on B by A}).

Common Types of Forces

• Gravity (F_g): Calculated as F_g = mg, where g ≈ 9.8 N kg^-1.

• Normal Force (F_N): Acts perpendicular to the surface contact.

• Friction (F_f): A force that actively resists motion between surfaces.

Force Vectors in Two Dimensions (2D)

• Components: F_x = F cos(θ), F_y = F sin(θ).

• Net Force Calculation:

  • Magnitude: F = √(F_x² + F_y²)

  • Angle: θ = tan^-1(F_y/F_x)

Forces on Inclined Planes

• Gravity Components (Relative to the slope):

  • Perpendicular to slope: F_N = mg cos(θ)

  • Parallel to slope (frictionless): F_net = mg sin(θ)

• With Friction: F_net = mg sin(θ) - F_f.

Example: Skier on a Frictionless Slope

Problem: A skier (mass m=90 kg) is on a frictionless slope inclined at θ=35°. Determine the resulting acceleration (a).