College Physics I: BIIG problem-solving method

1.  The Nature of Science and Physics

• The fundamental units are:  meter (m), kilogram (kg), and second (s).

• Accuracy of a measured value refers to how close a measurement is to the correct value.

• Precision of measured values refers to how close the agreement is between repeated measurements.

• The precision of a measuring tool is related to the size of its measurement the increments.

• Significant figures express the precision of a measuring tool.

• When multiplying or dividing measured values, the final answer can contain only as many significant figures as the least precise value.

• When adding or subtracting measured values, the final answer cannot contain more decimal places than the least precise value.

2.  Kinematic

• Kinematics is the study of motion without considering its causes.

• Displacement is the change in position of an object.

• Velocity is the rate of change of position.

• Acceleration is the rate of change of velocity.

• Deceleration is an acceleration with a direction opposite to that of the velocity.

• An object in free-fall experiences constant acceleration if air resistance is negligible.

• Graphs of motion can be used to analyze motion.

• The slope of a graph of velocity vs. time graph is acceleration.

3.  Two-Dimensional Kinematics

• The horizontal and vertical components of a vector are independent of one another.

• Projectile motion is the motion of an object through the air that is subject only to the acceleration of gravity.

• The maximum horizontal distance traveled by a projectile is called the range.

• Relative velocity is the velocity of an object as observed from a particular reference frame, and it varies with reference frame.

• Relativity is the study of how different observers measure the same phenomenon, particularly when the observers move relative to one another.

• Classical relativity is limited to situations where speed is less than about 1% of the speed of light (3000 km/s).

4.  Dynamics - Force and Newton’s laws of Motion

• Dynamics is the study of how forces affect the motion of objects.

• A free-body diagram is a drawing of all external forces acting on a body.

• Newton’s first law of motion states that a body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force.

• Newton’s second law of motion states that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass.

• Newton’s third law of motion states that whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that the first body exerts.

5.  Applications of Newton's Laws

• Friction is a contact force between systems that opposes the motion or attempted motion between them.

• A normal force is always perpendicular to the contact surface between systems.

• The magnitude of static (or kinetic) friction between systems stationary (or moving) relative to one another.

• Drag forces acting on an object moving in a fluid oppose the motion.

• Hooke’s law gives the relationship between the deformation and the applied force.

• For Young’s modulus, the applied force is parallel to the length.

• For Sheer modulus, the applied force is perpendicular to the length.

6.  Uniform Circular Motion and Gravitation

• Uniform circular motion is motion in a circle at constant speed.

• Centripetal acceleration is the acceleration experienced while in uniform circular motion.  It always points toward the center of rotation.

• Centripetal force is any force causing uniform circular motion. It always points toward the center of rotation.

• Rotating and accelerated frames of reference are non-inertial.

• Newton’s universal law of gravitation: Every particle in the universe attracts every other particle with a force along a line joining them.

• The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

• Newton’s law of gravitation applies universally.

7.  Work Energy and Energy Resources

• Work is the transfer of energy by a force acting on an object as it is displaced.

• The work-energy theorem states that the net work on a system changes its kinetic energy.

• Work done against gravity in lifting an object becomes potential energy of the object-Earth system.

• A conservative force is one for which work depends only on the starting and ending points of a motion, not on the path taken.

• The law of conservation of energy states that the total energy is constant in any process. Energy may change in form or be transferred from one system to another, but the total remains the same.

• Power is the rate at which work is done.

8.  Linear Momentum and Collisions

• Impulsive force is a large force exerted during small interval of time. Impulse is area under the force curve.

• System is a group of interacting particles. An isolated system is a system on which the net external force is zero.

• Law of conservation of momentum:  The total momentum of an isolated system is a constant.

• Collisions: Two or more particles come together. In a perfectly inelastic collision, they stick together and move with a common final velocity.

• Explosions:  Two or more particles move away from each other.

9.  Statics and Torque

• The first condition necessary to achieve equilibrium is that the net external force on the system must be zero.

• The second condition necessary to achieve equilibrium is that the net external torque on a system must be zero.

• By convention, counterclockwise torques are positive, and clockwise torques are negative.

• A system is said to be in stable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in a direction opposite the direction of the displacement.

• A system is in unstable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in the same direction as the displacement from equilibrium.

• The ratio of output to input forces for any simple machine is called its mechanical advantage.

10.  Rotational Motion and Angular Momentum

• Uniform circular motion is the motion with a constant angular velocity.

• In non-uniform circular motion, the velocity changes with time.

• The kinematics of rotational motion describes the relationships among rotation angle, angular velocity, angular acceleration, and time.

• The farther the force is applied from the pivot, the greater is the angular acceleration; angular acceleration is inversely proportional to mass.

• Angular momentum is conserved when net external torque is zero.

• Torque is perpendicular to the plane formed by radius and force and is the direction your right thumb would point if you curled the fingers of your right hand in the direction of force.

12.  Fluid

• Liquids and gases are both fluids.

• Pascal’s principle states that a change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container.

• Buoyant force is the net upward force on any object in any fluid.

• Archimedes’ principle states that the buoyant force on an object equals the weight of the fluid it displaces.

• Attractive forces between molecules of the same type (/different types) are called cohesive forces (/adhesive forces).

• Equation of continuity states that for incompressible fluids, flow rate at various points is constant.

• Bernoulli’s equation is a form of conservation of energy principle in terms of kinetic and potential energies for an incompressible, frictionless fluid

• Poiseuille’s law describes that the flow rate is proportional to the fourth power of the radius. 

13.  Temperature Kinetic Theory and Gas laws

• Temperature is related to the average kinetic energy of atoms and molecules in a system.

• Absolute zero is the temperature at which there is no molecular motion.

• Thermal equilibrium occurs when two bodies are in contact with each other and can freely exchange energy.

• Thermal expansion is the increase, or decrease, of the size (length, area, or volume) of a body due to a change in temperature.

• The ideal gas law relates the pressure and volume of a gas to the number of gas molecules and the temperature of the gas.

• Kinetic theory is the atomistic description of gases as well as liquids and solids.

• Kinetic theory models the properties of matter in terms of continuous random motion of atoms and molecules.

14.  Heat and Heat Transfer Methods

• Heat and work are the two distinct methods of energy transfer.

• Heat is energy transferred solely due to a temperature difference.

• Heat is transferred by three different methods: conduction, convection, and radiation.

• Heat conduction is the transfer of heat between two objects in direct contact with each other.

• Convection is heat transfer by the macroscopic movement of mass.

• Radiation is the rate of heat transfer through the emission or absorption of electromagnetic waves.

15.  Thermodynamics

• The internal energy of a system depends only on the state of the system and not how it reached that state.

• The first law of thermodynamics states that the change in internal energy of a system equals the net heat transfer into the system minus the net work done by the system.

• Entropy is also associated with the tendency toward disorder in a closed system.

• According to the second law of thermodynamics, the entropy of an isolated system always increases.

• A heat engine converts thermal energy from a hot reservoir into useful work.

• A heat pump uses work as input to transfer heat from a cold side to a hot side. 

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