AP PHYSICS C: MECHANICS
AP PHYSICS C: MECHANICS
|Linear Forms |Rotational Forms |
---------------------Kinematics---------------------
|[pic] = Position ([pic] - initial ; [pic] - final) |[pic] = Position ([pic] - initial ; [pic] - final) - radians |
|[pic] = Displacement |[pic] = Angular displacement ([pic] = arc length) |
|[pic] = Velocity ([pic] - initial ; [pic] - final) |[pic] = Angular velocity ([pic] - initial ; [pic] - final) |
|[pic] = Acceleration |[pic] = Angular acceleration |
|[pic] = Velocity of a with respect to b |[pic] = Radius |
| |[pic] = frequency (hertz --> Hz: amt. per sec.) |
| |[pic] = period (seconds) |
|Defnintion of [pic]: |Definition of [pic]: |
| [pic] | [pic] |
|Definitions of [pic] and [pic]: |Definitions of [pic] and [pic]: |
| [pic] | [pic] |
|Derivation (slope of tangent) to get [pic]/[pic]: |Derivation (slope of tangent) to get [pic]/[pic]: |
| [pic] | [pic] |
|Integration (area under graph) to get [pic]/[pic]: |Integration (area under graph) to get [pic]/[pic]: |
| [pic] | [pic] |
|Kinematic Equations 1&2: |Kinematic Equations 1&2: (by analogy to linear equivalents) |
|[pic] |Constant [pic] graph: |
|[pic] | [pic] |
| |Constant [pic] graph: |
|Equation of graph: | [pic] |
|(constant v) | |
|[pic] |Kinematic Equation 3: (by analogy to linear equivalent) |
|or alternatively: | [pic] |
| [pic] | |
|Equation of graph: |Kinematic Equation 4: |
|(constant a) |Combining 2 and 3 to eliminate [pic] yields: |
|[pic] |combining yields: [pic] |
|or alternatively |[pic] |
| [pic] |Connecting linear values to rotational ones: [pic] and [pic] are |
| |tangent to circle. |
|Kinematic Equation 3: | [pic] |
|[pic] |[pic] and [pic] are vectors along axis of rotation with direction |
|Sum of areas: |determined by right hand rule |
|[pic] |[pic] |
|Area of q: |Frequency & Period: |
| | [pic] |
|Area of r: | [pic] |
|[pic] | |
|Therefore: | |
|[pic] | |
| [pic] | |
| | |
|Kinematic Equation 4: | |
|Combining 2 and 3 to eliminate [pic] yields: | |
| [pic] | |
|[pic] | |
|Reference Frame Addition: [pic] | |
|[pic] reads as "velocity of a with respect to b." Treat | |
|x and y directions separately. | |
---------------------Forces/Torques---------------------
|[pic]= sum of the forces (Newtons) |[pic] = moment of inertia (rotational analog of [pic] for |
|[pic] = weight force (Newtons) |torques) Values of [pic]: |
|[pic] = normal force (Newtons) |Point mass moving in circle [pic][pic] |
|[pic] = friction force (Newtons) |Thin Hoop: [pic] |
|[pic] = coefficient of static friction |Rod length [pic] about its center [pic] |
|[pic] = coefficient of kinetic friction |Solid disk/cylinder radius [pic]: [pic] |
|[pic] = applied force (Newtons) |Solid sphere radius [pic]: [pic] |
|[pic] = tension force (Newtons) |Hollow sphere [pic] |
|[pic] = elastic force (Newtons) |[pic]= torque (analog of [pic]) |
|[pic]= centripetal acceleration ([pic]) |[pic] = angular momentum (analog of [pic]) |
|[pic]= acceleration due to gravity ([pic]) |[pic] = angular equivalent of impulse. Has no letter to represent |
|[pic] = momentum ([pic]) |it. (analog of [pic]) |
|[pic]= impulse ([pic]) | |
|Forces: |[pic](statics) |
|[pic] (statics) | [pic] (acceleration) |
| [pic] (acceleration) |Torque is a vector along the axis of rotation with direction |
|Treat x and y force components separately and then combine components |determined with right hand rule. |
|with Pythagorean theorem: |Parallel Axis Theorem: [pic] , where [pic] is the old moment of |
|[pic] |inertia, and [pic] is the distance between the old parallel axis of |
|[pic] |rotation and the new axis. |
|[pic] |[pic] |
|[pic] |Momentum & Impulse (by analogy): |
|Momentum & Impulse: | |
|[pic] [pic] |[pic] [pic] |
|[pic]Also... |Also... |
|[pic] | [pic] |
|[pic] |[pic] |
|(i.e. - Impluse is the area under a [pic]graph) | [pic] |
| |And... |
| | [pic] |
| |[pic] |
| |Calculating moments of inertia: |
| | [pic] |
---------------------Energy---------------------
|[pic] = Potential Energy (Joules) |[pic] = Rotational Kinetic Energy (Joules) |
|[pic] = Kinetic Energy (Joules) | |
|[pic] = Elastic Potential (Joules) | |
|[pic] = Work (Joules) | |
|[pic] = Power (Watts) | |
|[pic] indicates dot product | |
|[pic] |[pic] |
|[pic] [pic] [pic] | |
| [pic] | |
| [pic] | |
|Also, since [pic] | |
| [pic] | |
| [pic] (work done by field) | |
---------------------Center of Mass---------------------
(i.e. - sum of mass times position of all particles divided by sum of mass of all particles)
---------------------Gravity---------------------
• [pic] = semimajor axis length
• [pic] = apogee radius
• [pic] = perigee radius
• [pic] = universal gravitational constant [pic]
• [pic] = mass of larger object
• [pic] = mass of smaller object
• [pic] = distance between two objects OR radius of planet
• [pic] = distance to center of planet
• [pic] = velocity of orbiting object
• [pic] = escape velocity
[pic]
[pic] = constant for all orbits around same object
Fg adjusted for planetary motion:
[pic]
gravitational acceleration as a function of planet radius:
[pic]
gravitational acceleration as an object moves inside a planet:
[pic]
adjusted Eg for any location above planet's surface, r measured from center of planet:
[pic]
orbital velocity as a function of r:
energy is conserved throughout orbit (value is negative because it is bound):
[pic]
escape velocity (projectile launched perpendicular to earth's surface):
[pic], or in other words
[pic], and since [pic], then we can say
[pic], and thus,
[pic]
---------------------Simple Harmonic Motion (SHM)---------------------
[pic]
[pic]
[pic]
([pic] = angular frequency [pic])
[pic] and thus [pic]
By substitution, [pic]
Solving for angular frequency gives: [pic]
Substituting into [pic] gives [pic]
Period of a SHM pendulum (15 degrees or less):
[pic] = length of string
[pic]
---------------------Velocity Dependent Friction---------------------
terminal velocity = [pic]
[pic] = some constant that will be given to you or you will have to solve for
differential equation madness!
Example: [pic], where [pic] is a constant and [pic] is the velocity of the object going through air. Let's say it's falling from rest, and has mass [pic]. Find terminal velocity.
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
let [pic], so thus [pic], so [pic]
[pic]
MEMORIZE THIS: [pic]
[pic]
Constants of integration can really be combined into one constant of integration.
[pic]
[pic]
[pic]
[pic]
[pic]
note that when [pic], [pic], and thus [pic], so [pic]
[pic]
[pic]
[pic]
[pic]
note here that the constant is [pic]
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- ap physics 2 practice exam
- ap physics 2 questions
- ap physics practice test pdf
- ap physics 2 past exams
- ap physics 1 practice exam
- ap physics 2016 multiple choice
- ap physics rotational motion problems
- ap physics rotational kinematics
- ap physics 1 kinematic problems
- ap physics kinematics test
- ap physics 2 2017 frq
- 2019 ap physics 2 frq answers