TOOLS AND RULES

SELECTED TOOLS AND THE RULES THAT GO WITH THEM

(Arranged roughly in order of presentation as the course progresses)

Use trigonometry to find trigonometric functions of angles.

Use trigonometry to find components of vectors.

Use the Pythagorean theorem to find the magnitude of a vector from its components.

The magnitude of a vector is never negative.

Add vectors by adding components of the same kind separately to find the components of the sum.

To find the angle between two vectors you must first put their tails together.

You can use one or more of the kinematics equations only if the acceleration vector is constant.

Select the kinematics equation that relates the one thing that you are looking for to things that you already know or can find.

If two (or more) objects are in motion, write one equation for each object expressing its position at any time t.

If the position of an object is known at some specific time, write an equation that puts it there at that specific time.

The majority of projectile motion problems can be solved by first finding the time of flight.

The time of flight can be found by placing the projectile where you know it to be after time equal to the time of flight has elapsed.

Each projectile needs two equations, one for the x-component of the position vector at any time t and one for the y-component of the position vector at any time t.

The acceleration of gravity has no horizontal component.

At maximum height, the vertical component of the velocity is zero.

To find the velocity of B relative to A, add vectorially the negative of A's velocity to B's velocity.

The net force is in the same direction as the acceleration; the acceleration is in the same direction as the net force.

If the net force is zero, the acceleration is zero; if the acceleration is zero, the net force is zero.

Contact forces adjust themselves to provide the observed acceleration up to a certain upper limit that they cannot exceed.

If you start a free body diagram, finish it following the standard recipe and without skipping any steps or cutting corners.

"Frictionless" means that a surface can exert a force only in a direction perpendicular to it.

Static friction is a contact force component that adjusts itself to provide the observed acceleration, but only up to a limit. The direction of static friction may or may not be opposite to the velocity of the system but is always parallel to the surface.

Kinetic friction is a contact force component that always adjusts its direction opposite to the velocity of the system and parallel to the surface.

To find the work done by a constant force on a system as the system is displaced from point A to point B, you need to multiply three things: the magnitude of the force, the magnitude of the displacement and the cosine of the angle between the force and displacement.

If only conservative forces act on a system as it is displaced from point A to point B, use Mechanical Energy Conservation, otherwise use the Work-Energy Theorem.

All collisions conserve linear momentum.

Linear momentum is conserved as long as there is no net external force acting on the center of mass.

A collision does not conserve energy unless there is language that says it is so.

Collisions in which two masses stick together and move as one (perfectly inelastic collisions) never conserve energy.

Explosions are perfectly inelastic collisions with time running backwards: they never conserve energy but they conserve linear momentum.

External forces act at the center of mass.

Any problem in rotational kinematics can be transformed to a linear kinematics problem that is, sometimes, easier to visualize.

When there is angular acceleration, the period and frequency are meaningless.

To find a torque you need a force and a position vector; to specify a position vector you need an origin.

When the net torque is zero, any origin will do. If you choose as origin a point where one more or more forces are applied, you will have fewer torques to calculate.

The centripetal component of the linear acceleration is responsible for changing the direction of the velocity and causes the object to turn. It is zero when the angular velocity is zero.

The tangential component of the linear acceleration is responsible for changing the speed and causes the object to speed up or slow down. It is zero when the angular acceleration is zero.

When the net torque is zero, the angular acceleration is zero; when the angular acceleration is zero, the net torque is zero.

When you use the rotational analog of Newton's Second Law, express the moment of inertia about an axis passing through the origin that you used to express the net torque.

The total kinetic energy of a rotating object can always be written as 1/2(I ω²) where I is the moment of inertia about the axis of rotation.

Angular momentum is conserved as long as there is no net external torque acting on the system.

When objects float in fluids, first draw a free body diagram calling the buoyant force BF, write Newton's Second Law Equations, then re-express BF as the weight of the displaced fluid.
In most harmonic oscillator problems it is usually helpful to find the angular frequency omega as a first step.
Vertical springs may be treated just like horizontal springs with the equilibrium position shifted to a new point.
The kinematics equations are absolutely inappropriate to use for harmonic motion.
In standing wave problems draw a diagram with the correct number of nodes. Then figure what fraction of the wavelength is the length of the string (or tube for sound waves) and then relate the wavelength to the frequency and speed of propagation.
To effect a phase transition in a substance, you need first to bring the substance to the appropriate phase transition temperature. In other words, an ice cube has to reach zero degrees Celsius before it will start melting.
When an ideal gas goes from state A to state B, the work done by the gas and the heat added to the gas depend on how the gas gets from A to B.
When an ideal gas goes from state A to state B, the change in internal energy is the same regardless of how the gas gets from A to B.
A gas always does positive work on the environment when it expands and negative work when it is compressed.
If you know how a gas gets to point B from point A, you should use the Ideal Gas Law and the First Law of Thermodynamics to figure out the sign of the change in internal energy and whether heat is added or removed from the gas.
The First Law of Thermodynamics is a statement of the simple fact that "What stays in is what goes in minus what comes out".
Negative heat added to a gas is positive heat removed from the gas.
The work done by a gas is represented as an "area under the curve" on a pV diagram.