Physics

Kinematics Basics

• Distance vs. Displacement:

  • Distance is always positive.

  • Displacement can be positive or negative.

  • Example: Distance = 6m, Displacement = -6m (moving back to start).

• Axes:

  • Y-axis: Positive means moving up; negative means moving down.

  • X-axis: Calculated as ( X_f - X_i ) or ( X_2 - X_1 ).

  • Y-movement: ( Y = Y_f - Y_i ), with time ( t = t_f - t_i ).

• Speed: Average speed is always positive, defined by:

  • ( V_{avg} = \frac{\text{distance traveled}}{\text{time}} )

• Velocity:

  • Velocity can be negative when moving in negative direction (like left or down).

  • Average velocity in both x and y directions: ( V_{x0} = 0 ), ( V_{y0} = 0 ).

Acceleration

• Definition: Acceleration measures the change in velocity over time.

• Formula: ( a = \frac{V - V_0}{t} )

• Units: m/s².

• Examples:

  • If ( V = -3m/s ) and ( a = -2m/s² ), this indicates slowing down.

  • If velocity and acceleration have the same sign, the object is speeding up.

  • If they have opposite signs, the object is slowing down.

Motion Analysis

• Variables:

  • Initial Velocity ( V_0 )

  • Final Velocity ( V_f )

• Gravity: The acceleration due to gravity is ( g = 9.8 m/s² ).

• Projectile motion: The symmetry in projectile motion dictates timings for upward and downward paths.

Forces and Newton's Laws

• Newton's Second Law: ( F = ma )

• Free Body Diagram: Important for analyzing forces acting on an object.

• Weight: The weight of an object determines its gravitational force which is ( F_g = mg ).

Friction

• Friction Types:

  • Static friction (fs) is generally higher than kinetic friction (fk).

• Friction Coefficient:

  • Coefficient of static friction (( , \mu_s )) is dimensionless.

  • Kinetic friction is usually less than static friction.

Energy

• Work: Work done by a force can be positive or negative, depending on the direction of motion.

  • Formula: ( W = Fd \cdot cos(\theta) )

• Kinetic Energy (KE): ( KE = \frac{1}{2} mv^2 )

• Potential Energy (PE): ( PE = mgh )

• Energy Conservation: ( KE_i + PE_i = KE_f + PE_f )

Momentum and Collisions

• Momentum: ( P = mv )

• Conservation of Momentum: In elastic and inelastic collisions, momentum is conserved.

• Impulse: ( J = \Delta P = F \cdot t )

Torque and Equilibrium

• Torque: Calculated as ( T = F \cdot r \cdot sin(\theta) )

• Static Equilibrium: For an object at rest, net forces and net torques must be zero.