Exam 3 Equation Sheet

✅ Exam Notes — N1 to N7

✅ N1 — Motion & Newton’s 2nd Law

🔹 Newton’s 2nd Law (Center of Mass)

• The net external force equals the total mass times the acceleration of the center of mass.

🔹 Definitions

• Velocity = rate of change of position.

• Acceleration = rate of change of velocity.

✅ N2 — Fundamental Forces

🔹 Gravitational Force

• Attractive force between two masses.

• (G): universal gravitational constant

• (r): separation between masses

🔹 Electric Force (Coulomb’s Law)

• Force between two charges.

• Attractive or repulsive depending on sign.

🔹 Spring Force (Hooke’s Law)

• Force exerted by a spring.

• Direction pulls toward equilibrium length r0.

✅ N3 — Kinematics

🔹 Constant acceleration

• Straight-line motion at constant acceleration.

• Position function under constant acceleration.

🔹 General motion — Integrals

• Velocity is the integral of acceleration.

• Position is the integral of velocity.

✅ N4 — Torque

• Torque is a rotational analog of force.

• Depends on angle between vectors r and F.

• Maximum torque occurs at 90 degrees.

✅ N5 — Friction & Drag

🔹 Static Friction

• Prevents motion.

• Increases up to a maximum value.

🔹 Kinetic Friction

• Opposes motion once sliding begins.

🔹 Drag Force

• Opposes motion through fluid.

• Depends on speed, cross-sectional area, drag coefficient, density.

✅ N7 — Circular Motion

🔹 Constant Speed

• Speed around a circular path.

• R = radius, T = period.

🔹 Uniform Circular Motion

• Acceleration points radially inward (centripetal).

🔹 Nonuniform Circular Motion

• Acceleration has:

  • Tangential part (speed change)

  • Radial part (direction change)

✅ Quick Summary Table