F=ma Exam Concepts
Click on a bulleted item (e.g. Vectors) to practice problems related to the concept.
Click on a numbered item (e.g. Kinematics) to practice problems related to the topic.
1. Kinematics
- Vectors (components, position, displacement, velocity)
- Speed vs. velocity
- Average vs. instantaneous (velocity, speed)
- Motion graphs (x-t plot, v-t plot, a-t plot, v-x plot, a-x plot)
- 5 kinematics equations
- General kinematics equations (finding x(t), v(t))
- Free fall (gravitational acceleration)
- Projectile motion (horizontal motion, vertical motion, symmetry, time of flight, range equation, height equation)
- Circular motion (centripetal acceleration/force, tangential/total acceleration)
- Relative velocity (velocity-addition formula)
2. Dynamics
- Statics (balancing forces, balancing torques, choosing pivot point)
- Newton’s laws
- Forces in mechanics (normal force, friction force, static vs. kinetic, weight, tension, spring force)
- Effective spring constant (parallel, series, cutting)
- Vertical spring (shifted equilibrium, potential energy)
- Cutting strings vs. springs
- Inclined plane (rotate axes, forces, slip angle)
- Atwood machine (conservation of string)
- Scale reading (normal force)
- Fictitious forces (inertial force, centrifugal force)
- Coriolis force
- Equivalence principle
- Artificial gravity (rotating spaceship, simulating weightlessness)
- Air resistance (linear drag, quadratic drag, terminal velocity)
3. Energy
- Kinetic energy (translational, rotational, relation to momentum)
- Work (general expression)
- Work-energy theorem (kinetic, potential)
- Potential energy graphs (force)
- Types of equilibrium
- Spring potential energy (Hookian, non-Hookian)
- Conservation of energy (closed system, open system)
- Energy dissipation (kinetic friction, breaking a spring)
- Power (average, instantaneous)
- Block on conveyor belt
4. Collisions
- General Newton’s 2nd law
- Conservation of linear momentum (no external forces, 1D, 2D, 3D)
- Impulse-momentum theorem
- 1D inelastic collision (perfectly inelastic, wall collisions)
- 1D elastic collision (wall collisions)
- Law of reflection (elastic collision)
- Ballistic pendulum (momentum conservation, angular momentum conservation)
5. System of Masses
- Center of mass (discrete, continuous, replacing object with point)
- Dynamics of CM (v_CM, a_CM)
- CM frame (no momentum)
- Torque from weight (CM, principle of superposition)
- Pulleys with rotational inertia
- Reduced mass
6. Rigid Bodies
- Angular kinematics (angular velocity, angular acceleration, kinematics equations)
- Velocity constraints (rotating rigid object, rods)
- Moments of inertia (principle of superposition, points, hoop, disk, solid/hollow sphere, rod about center/end, fluids)
- Parallel-axis theorem
- Perpendicular-axis theorem
- Recursion for rotational inertia
- Torque (moment arm)
- Rotational Newton’s 2nd law
- Angular momentum (translational, rotational, vector)
- Conservation of angular momentum (no external torques)
- Rolling motion (rolling without slipping)
- Rolling down inclined plane (acceleration, slipping angle)
- General kinetic energy
- General angular momentum
7. Oscillatory Motion
- Simple harmonic motion (angular frequency, period)
- Mass-spring system (angular frequency, period)
- Simple pendulum (angular frequency, period)
- Physical pendulum (angular frequency, period)
8. Gravity
- Gravitational force (principle of superposition, gravitational field)
- Gauss’s law for gravity (shell theorem, spherical symmetry, cylindrical symmetry)
- Gravitational potential energy (constant field, general expression)
- Binding energy (sphere)
- Escape velocity
- Kepler’s laws
- Circular orbits (orbit velocity, angular momentum, energy)
- Elliptical orbits (ellipse properties, orbit velocity, angular momentum, energy, vis-viva equation)
- Parallax
9. Fluids
- Pressure with depth (atmospheric pressure, gauge pressure)
- Pascal’s law
- Buoyant force (Archimedes’ principle, apparent weight, CM of fluid, effective gravity)
- Floating (fraction)
- Continuity equation
- Bernoulli’s principle
- Toricelli’s law
- Surface tension
10. Other
Problem-solving techniques, elasticities, waves, data analysis
- Dimensional analysis (base dimensions, measurements)
- Limiting cases
- Small angle approximation
- Young’s modulus
- Bulk modulus
- Tensile strength
- Wave speed in string
- Standing waves (fundamental mode)
- Data expression (log plot, log-log plot)
- Error propagation (standard deviation, addition, multiplication, power)