Mechanics Review
Kinematics:
● Kinematic Equations (in one dimension):
(Note: the first two equations work for any situation, but the last three can only be used in
cases of constant acceleration.)
● The difference between distance, displacement, average speed, instantaneous speed,
average velocity, and instantaneous velocity
● How to write descriptions of motion using position vs. time graphs or velocity vs. time graphs
● The relationships between position, velocity, and acceleration graphs (you should be able to
produce any of the graphs when given another graph or the description of motion)
● The relationship between the direction of the velocity and the direction of the acceleration for
an object that is speeding up or slowing down
Dynamics:
● Gravitational Force/Weight: 𝐹𝑔 = 𝑚𝑔
(g = gravitational field strength = 9.8 N/kg near the surface of Earth)
● Mass vs. Weight (what is the difference?)
● Freebody Diagrams: label the forces using the F_ (on ___ by ___) notation
● Newton's First Law of Motion: the velocity of an object remains constant unless a net force
acts on the object
● Newton's Second Law of Motion: Σ𝐹 = 𝑚𝑎
● Newton's Third Law of Motion: the force that object A exerts on object B is equal in
magnitude and opposite in direction to the force that object B exerts on object A (labeling
forces properly will help you to identify 3rd Law force pairs)
● The relationship between the directions of velocity, acceleration, and net force
● Determining the x- and y-components of a force vector
● Frictional Force: always acts parallel to the surfaces and is proportional to the FN exerted
between the surfaces and depends on the types of surfaces
● 𝐹𝑠(𝑚𝑎𝑥) = µ𝑠𝐹𝑁 and 𝐹𝑘 = µ𝑘𝐹𝑁
● For one-body problems, start by making a freebody diagram. If the object is at rest or
moving at a constant velocity, choose a coordinate system that requires you to break up the
least number of forces (this may mean that you need to rotate your coordinate system). If
the object is accelerating, choose a coordinate system such that one of the axes points in
the direction of the acceleration. Next, write equations for the sum of the forces in the x- and
y-directions. If the system is accelerating and you have chosen your co-ordinate system
wisely, then the object will only be accelerating in one direction. If the system is moving at a
constant velocity or is not moving in the x- and/or y-direction, then the net force in that
direction will be zero.
● For two-body problems, you will need to use the same strategies as outlined for one-body
problems, but you will also need to think about force pairs (Newton’s 3rd Law) and how you
define your system.
Projectile Motion:
● Determining the x- and y-components of a velocity vector
● If Fg is the only force acting on the object (the definition of projectile motion/freefall):
1. ax = 0, which means that the velocity in the x-direction does not change
2. ay = –g, which means that (near the surface of Earth) ay = –9.8 m/s2
● The equations for Projectile Motion are simply the kinematic equations, but it is vitally
important that you add the appropriate x or y subscripts to each equation (for example,
ay = ∆vy/∆t).
Circular Motion:
● An object in uniform circular motion has a constant speed but a changing velocity (since the
direction of the velocity is changing), thus it is accelerating.
● The magnitude of the acceleration can be calculated using
.
● The direction of the net force acting on an object undergoing uniform circular motion points
towards the center of the object’s circular path.
● The direction of the acceleration also points towards the center of the circle (since net force
and acceleration always point in the same direction).
● The direction of the velocity is tangent to the circle (perpendicular to the acceleration and net
force).
● T = period = time to go around the circle once
Momentum:
● Momentum (p) = mv (Note: momentum is a vector and has a direction!)
● Conservation of Momentum: Δpsystem + Δp surroundings = 0
● If you define the system such that the net impulse imparted to the system is zero, then
pi (system) = pf (system). For a collision, if you define the system to be all of the colliding
objects, then you can reasonably estimate that the momentum of the system the instant
before the collision is equal to the momentum of the system the instant after the collision.
Energy:
● Use energy pie charts or bar graphs to analyze the internal energy changes of a system.
(Note: your choice of system plays a big role in energy “accounting” and affects the types
and quantity of energy in the system.)
● Earth must be one of the objects in the system in order for the system to have Eg. If Earth is
part of the system, make sure to show where you have set Eg (or h) = 0.
● A spring (or similar object) must be one of the objects in the system in order for the system
to have Eel.
● Conservation of Energy: ΔEsystem + ΔE surroundings = 0
● Work changes the energy of a system and depends on the force exerted and the
displacement of the object (specifically, the components of the force and the displacement
that are parallel to each other). Note: only objects that are not in the system can do work on
the system.
● If you define the system such that the net work done on the system is zero, then
Ei (system) = Ef (system).
● When is the work done on a system positive? negative? zero? What happens to the
energy of the system in each case?