Ch. 1: Kinematics and Dynamics Flashcards
SI Units
Related to the metric system include meter, kilogram, second, ampere, mole, kelvin, and candela
Vectors
Physical quantities that have both magnitude and direction. Include displacement, velocity, acceleration, and force, among others
Scalars
Quantities without direction. May be the magnitude of vectors (like speed) or may be dimensionless, like coefficients of friction
Vector addition
Use the tip to tail method or break vector into components, add x components and add y components to get x and y components of resultant vector and use the Pythagorean theorem to find resultant
Vector subtraction
change the direction of the subtracted vector and then follow the procedures for vector addition
Finding the x and y components of a vector
x= Vcosθ
y= Vsinθ; θ is angle between x component and vector
If we know x and y we can find V using pythagorean theorem
Multiplying a vector by a scalar
Changes the magnitude and may reverse the direction
Multiplying a vector by a vector
Dot product: scalar quantity, product of the vectors magnitudes and the cosine of the angle between them
Cross product: vector quantity. Product of the vectors magnitudes and the sine of the angle between them. Right hand rule is used to determine direction of resultant vector
Displacement
Vector representation of a change in position. Path independent and is equivalent to the straight line distance between the start and end locations
Distance
Scalar quantity that reflects the path traveled
Velocity
Vector representation of the change in displacement with respect to time
Average velocity
Total displacement divided by total time
Average speed
Total distance divided by total time
Instantaneous velocity
Limit of the change in displacement over time as the change in time approaches 0
Instantaneous speed
Magnitude of the instantaneous velocity vector
Force (F)
Any push or pull that has the potential to result in an acceleration. SI unit for force is newton (N) = (kg*m)/s^2
Gravity
Attractive force between 2 objects as a result of their masses
Gravitational force
Fg = (Gm1m2)/r^2; m1 = mass of object 1, m2 = mass of object 2, G is universal gravitational constant, r =dist between centers of mass
Friction
Force that opposes motion as a function of electrostatic interaction at the surfaces of 2 objects
Static friction (fs)
Exists between two objects that are not in motion relative to each other– can take on many values depending on magnitude of an applied force
Coefficient of static friction
Unitless quantity that is dependent on the two materials in contact
0 ≤ fs≤usN; us = coefficient of static friction, N=magnitoude of normal force
Normal force
Component of the force between two objects in contact that is perpendicular to the plane of contact between the object and the surface upon which it rests
Kinetic friction (fk)
Exists between two objects that are in motion relative to each other, a sliding object and surface over which object slides; constant value=ukN=f
Coefficient of friction
Depends on the two materials in contact. The coefficient of static friction is always higher than the coefficient of kinetic friction.
Mass (m)
Measure of the inertia of an object– amt of matter in the object. Scalar quantity so only has a magnitude. SI unit is kilogram (kg), independent of gravity
Weight (Fg)
Force experienced by a given mass due to its gravitational attraction to the earth, vector quantity w units in newtons (N), weight of an object can be thought of as being applied at a single point in that object called the center of mass or gravity
Relation between weight and mass
Fg= mg; g is acceleration due to gravity (9.8 m/s^2)
Acceleration
Vector representation of the change in velocity over time. Average or instantaneous acceleration may both be considered, similar to velocity. Average acceleration is defined as ā = Δv/Δt; instantaneous acceleration is defined as avg acceleration as Δt approaches 0
Newton’s first law
Law of inertia: states than an object will remain at rest or move with a constant velocity if there is no net force on the object
Newton’s second law
States that any acceleration is the result of the sum of the forces acting on the object and its mass
Newton’s third law
States that any 2 objects interacting w one another experience equal and opposite forces as a result of their interaction
Linear motion
Includes free fall and motion in which the velocity and acceleration vectors are parallel or anti parallel
Air resistance
Opposes the motion of an object; object in free fall will experience a growing drag force as the magnitude of its velocity increases. Eventually this drag force will be equal in magnitude to the weight of the object nand the object will fall with constant velocity according to Newton’s first law; this velocity is called terminal velocity
Projectile motion
Contains both an x- and y- component. Assuming negligible air resistance, the only force acting on the object is gravity
Inclined planes
Example of 2D motion. Easiest to consider the dimensions as being parallel and perpendicular to the surface of the plane
Circular motion
Has radial and tangential dimensions. Fc = (mv^2)/r
Uniform circular motion
only force is centripetal force pointing radially inward. Instantaneous velocity vector always points tangentially
Dynamics
Study of forces and torques
Free body diagram
Representations of the forces acting on an object. Useful for equilibrium and dynamics problems
Translational Equilibrium
Occurs in absence of any net forces acting on an object. An object in translational equilibrium has a constant velocity, and may or or may not also be in rotational equilibrium
First condition of equilibrium
Translational equilibrium only exists when vector sum of all of the forces acting on an object is 0 (same as newton’s first law)
Rotational equilibrium
Occurs in the absence of any net torques acting on an object. Rotational motion may consider any pivot point, but the center of mass is most common. An object in rotational equilibrium has a constant angular velocity– on mcat, usually 0
Fulcrum
Fixed pivot point around which an object rotates
Torque
Application of force at some distance from the fulcrum generates torque or the moment of force. Distance between applied force and the fulcrum is the lever arm. Torque generates rotational motion, not application of force itself
