Physics Textbook Flashcards
What is Hooke’s Law?
F = kΔx
F = force
k = spring constant
Δx = change in length of spring
What is the equation for angular acceleration?
α = Δω / Δt
What conditions must be true in order for Kepler’s laws to hold true?
- The smaller body must have a much smaller mass than the larger body that it orbits.
- The system must be isolated from other masses (must be far away from other planets).
What is the equation that relates acceleration to displacement?
Δx = ½at2 + v0t
Define displacement.
It is a vector quantity that includes distance AND direction.
Example = When a brick is moved 5 meters to the right, it was displaced 5 meters to the right.
What condition is required in order for angular momentum to be conserved in a system?
The net external torque on the system must be zero.
What is Kepler’s second law?
Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal times.
What is the equation for mechanical advantage?
MA = Fout / Fin
What is the equation that relates torque to angular momentum?
τnet = ΔL / Δt
L = angular momentum
Name the 3 criteria that must be met in order for the laws of classical physics to apply.
- Matter must be moving at speeds < ~1% of the speed of light.
- The objects dealt with must be large enough to be seen with a microscope.
- Only weak gravitational fields (such as the field generated by the Earth) can be involved.
What is Kepler’s first law?
The orbit of each planet about the Sun is an ellipse with the Sun at one focus.
What is 180° in radians?
π
What is the equation for rotational work?
Wnet = τnetθ
What is the equation for efficiency?
Eff = Wout / Ein
Efficiency = Useful work output, divided by energy consumed.
Define bulk modulus. What is the equation for it?
The change in volume due to an evenly-applied force on all sides of an object.
ΔV = (FV0) / (BA)
F / A = force per area, applied uniformly inward on all surfaces
B = bulk modulus (unique for each material)
How do you determine the mechanical advantage of a pulley system?
The number of cables pulling directly upward on the system of interest is approximately equal to the MA of the pulley system.
What units can Newtons be broken down into? In other words, what are the “components” of 1 Newton?
1 N = 1 kg m / sec2
Define shear deformation. What is the equation for it?
Change in shape of an object, due to a perpendicular (sideways) force.
Δx = (FL0) / (SA)
Δx = change in sideways shape of object, perpendicular to L
F = applied force (perpendicular to L)
L0 = length of object
S = Shear modulus
A = cross-sectional area
On a plot of velocity vs time, the slope of the curve represents what value?
The acceleration at a given point in time.
What is the equation for gravitational potential energy?
ΔPEg = mgh
What is the equation for the optimum angle of an ideally banked curve (one in which you can still make the turn, even in a frictionless environment).
θ = tan−1 (v2 / (rg))
What is the right-hand rule, as it applies to angular momentum?
Take your right hand, and curl your fingers in the direction of rotation. Your outstretched thumb points in the same direction as the vectors for L and ω.
Define neutral equilibrium, and give an example.
A system is in neutral equilibrium if its equilibrium is independent of displacements from its original position.
Example = A marble on a flat horizontal surface.
Name the 4 basic forces.
For each one, state whether it is attractive, repulsive, or both.
- Gravitational (attractive only).
- Electromagnetic (both).
- Weak nuclear (both).
- Strong nuclear (both).
What are the 2 equations that let you calculate the magnitude of centripetal acceleration?
ac = v2 / r
ac = r ω2
What is the equation that relates angular acceleration to tangential acceleration?
at = r α
at = tangential acceleration
r = radius
α = angular acceleration
What are the unit vectors? What letters are used to represent them?
i represents the unit vector in the x direction (it is 1 unit long).
j represents the unit vector in the y direction (it is 1 unit long).
What is 60° in radians?
π / 3
What is 90° in radians?
π / 2
What is the definition of power?
Power = Work / Time
What is the equation that relates linear velocity to angular velocity?
v = r ω
v is the linear velocity
ω is the angular velocity
r is the radius (length from center to point where v is being measured)
What is the work-energy theorem?
Wnet = ½mvf2 − ½mvi2
The net work done is equal to the change in kinetic energy.
What is the definition of a Watt?
1 W = 1 J / sec
The Watt is a unit of power.
Define moment of inertia.
I = ∑mr2
Moment of inertia (I) is the sum of mr2 for all the point masses that it is composed of.
I is analogous to m in translational motion.
What is Newton’s Second Law?
F=ma
F and a are vector quantities, so they have arrows over the letters.
Define normal force.
Normal force = the force that acts on a resting object, which acts perpendicular to the surface that the object is resting on.
Example = if a block is resting on a ramp, the normal force points in a direction perpendicular to the ramp, NOT straight up.
Describe inelastic collisions. What is conserved?
The two objects that have collided are not stuck together, but some deformation / loss of energy has occurred.
Momentum is conserved.
Kinetic energy is not conserved.
Explain the example about rolling soup cans down a ramp, and give the equation for it.
If the soup is very thick, the can will not roll as quickly as a can that has thinner soup, even if the total masses are equal. This is because the thick soup rotates inside the can (it gains translational and rotational KE), but the thin soup does not rotate inside the can (it gains translational KE only).
PEgrav = KEtrans + KErot
What quantity is represented by the area under the curve in a graph of spring force vs distance?
The work done to displace the spring.
What are the 2 conditions that must be met, in order for a system to be in equilibrium?
Fnet = 0
τnet, external = 0
The net force must be zero, and the net external torque must be zero.
What is the equation for potential energy of a compressed spring?
PEs = ½ k x2
k is the spring’s force constant
x is the displacement of the spring from its resting position
What is the equation that relates forces in a hydraulic system?
F1 / A1 = F2 / A2
How does pressure due to surface tension change with increasing radius? How does this relate to emphysema?
Alveolar walls of emphysema victims deteriorate, and the sacs combine to form larger sacs. Because pressure produced by surface tension decreases with increasing radius, these larger sacs produce smaller pressure, reducing the ability of emphysema victims to exhale. A common test for emphysema is to measure the pressure and volume of air that can be exhaled.
What is the equation that lets you find the fraction of an object submerged floating in a fluid?
Frac. subm. = ρobj / ρfluid
ρobj = avg density of object
ρfluid = density of fluid
Define strain, in terms of physics.
The ratio of change in length to length (ΔL/L0) is defined as strain (a unitless quantity).
What is the equation that relates stress, strain, and Young’s modulus?
(Stress) = (Y) x (Strain)
This is just a rearrangement of the main equation for the stretching of a rope under tension.
What is the equation for power in fluid flow?
(P + ½ρv2 + ρgh) Q = power
Q = flow rate
Multiply Bernoulli’s equation by flow rate, and you get power.
What is 30° in radians?
π / 6
Define centrifugal force.
It is a fictitious force, that “pushes” objects toward the outside (example = centrifuges). In reality, there is no force that does this.
What is the equation that relates radians to revolutions?
2π rad = 1 revolution
What is the equation for surface tension?
γ = F / L
Surface tension γ is defined to be the force F per unit length L exerted by a stretched liquid membrane.
What is Bernoulli’s equation?
P1 + ½ρv12 + ρgh1 = P2 + ½ρv22 + ρgh2
Define stress, in terms of physics.
The ratio of force to area (F/A) is defined as stress measured in N/m2.
What is Newton’s First Law?
Objects at rest tend to stay at rest, and objects in motion tend to stay in motion, unless acted upon by an unbalanced outside force.
What is the equation that describes how much a rope or pipe will stretch under tension?
ΔL = (FL0) / (AY)
ΔL = change in length
F = applied force of tension
L0 = initial length
A = cross-sectional area
Y = Young’s modulus (elastic modulus), a unique constant for each material
Describe Reynold’s number. How is it calculated? What does this tell you?
NR = (2ρvr) / η
ρ = density of fluid
v = speed of fluid
r = radius of tube
η = viscosity
NR < 2,000 = Laminar flow
NR > 3,000 = Turbulent flow
Define unstable equilibrium, and give an example.
A system is in unstable equilibrium if, when displaced, it experiences a net force or torque in the same direction as the displacement from equilibrium.
Example = a ball at the top of a hill.
What is Poiseuille’s Law?
Q = (πΔPr4) / (8ηl)
Q = flow rate
ΔP = difference in pressure
r = radius
η = viscosity
l = length
What condition is required in order for linear momentum to be conserved in a system?
The net external force on the system must be zero.
What equation relates the period and radius of a satellite’s orbit about a larger body M?
T2 = ( 4π2 r3 ) / ( GM )
Define stable equilibrium, and give an example.
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 to the direction of the displacement.
Example = a marble at the bottom of a bowl.
How do joules relate to Newtons?
1 J = 1 N m
What is the difference between inertial and non-inertial reference frames?
An inertial reference frame is one in which the body has no net forces acting on it, and thus is not accelerating. Earth can almost be considered an inertial reference frame (exception: Coriolis Force).
A non-inertial reference frame is one in which the body is experieincing acceleration. This can cause objects within the frame to experience fictitious forces. Examples: being in a turning car, centrifuges, merry-go-rounds, etc.
What is the equation that includes acceleration, velocity, and distance, but does not include time?
vf2 = vi2 + 2aΔx
What is a conservative force?
It is a force that only depends on the initial and final positions of the mass, but NOT on the path taken.
Conservative forces conserve mechanical energy.
Non-conservative forces do NOT conserve mechanical energy.
Examples of conservative forces: Gravity, springs.
Examples of non-conservative forces: Friction, drag.
What is Kepler’s third law?
TA2 / TB2 = rA3 / rB3
The ratio of the squares of the periods (TA and TB) of any two planets about the Sun is equal to the ratio of the cubes of their average distances from the Sun (rA and rB).
Define impulse, and give the equation for it.
Impulse = change in momentum
Δp = FnetΔt
What is the equation for calculating the center of gravity in one dimension?
XCG = (m1x1 + m2x2 + …) / (m1 + m2 + …)
In other words, multiply each mass by its position, add them all up, and then divide by the total mass.
What is the equation that relates rotational work to moment of inertia?
Wnet = Iαθ
I = moment of inertia
What is the equation for torque?
τ = r F sin(θ)
τ = torque (Greek letter tau)
r = distance from pivot point to point where force is applied
F = magnitude of force applied
θ = angle between the force and the vector directed from the point of application to the pivot point (θ=90° if perpendicular)
What is the equation for the coefficient of kinetic friction?
µK = ║Ff║ / ║FN║
The force of kinetic friction = the magnitude of the force of friction / the magnitude of the normal force
What are the 3 types of equilibrium?
Stable, unstable, and neutral.
What is the equation for angular momentum?
L = Iω
I = moment of inertia
On a plot of velocity vs time, the area under the curve represents what value?
Distance travelled.
How many Watts are equal to 1 horsepower?
1 hp = 746 Watts
What is the equation for the force of gravity between two objects?
F = (G M1 M2) / r2
G = Gravitational constant (6.67 x 10-11 N m2 / kg2)
M1 and M2 = masses of the objects (in kg)
r = distance between objects (in meters)
What is the equation for drag force?
FD = ½CρAv2
C = the drag coefficient (a unique constant for each object)
ρ = the density of the fluid
A = the cross-sectional area of the object
v2 = velocity2 (relative to the flow of the fluid)
What is the difference between a vector and a scalar?
Vectors have a magnitude AND a direction.
Scalars have a magnitude ONLY, but NO direction.
What is the equation that relates torque to moment of inertia?
τnet = αI
Define centripetal force.
Any net force that causes uniform circular motion.
What is the definition and equation for angular velocity?
ω = (Δθ) / (Δt)
Angular velocity is the rate of change of an angle.
What is Newton’s Third Law?
Every force must be opposed by an equal and opposite force.
What is the equation that you can use to calculate pressure at a particular depth in a fluid?
P = ρgh
ρ = density of the fluid
g = acceleration due to gravity
h = depth
What is Pascal’s Principle?
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.
Describe perfectly inelastic collisions. What is conserved?
The two objects that have collided are now stuck together.
Momentum is conserved.
Kinetic energy is not conserved.
Describe laminar flow.
Laminar flow is characterized by smooth flow of fluid in layers that do not mix.
What are the units for radians?
Radians are unitless (they are defined as a ratio of distance).
What is the equation of continuity?
A1v1 = A2v2
<span>A = cross-sectional area of pipe/tube</span>
<span>v = velocity of fluid</span>
Define torsion.
The twisting of an object, due to an applied torque.
What is the equation for rotational kinetic energy?
KErot = ½ I ω2
I = moment of inertia.
Define centripetal acceleration.
It is the acceleration of an object in uniform circular motion (due to a net force that acts inwards).
What is Archimedes’ Principle?
FB = wfluid
The buoyant force (FB) is equal to the weight of the fluid displaced by the object (wfluid).
What is a Pascal?
It is a unit of pressure. 1 Pa = 1 N / m2
What is the equation that relates force to momentum?
Fnet = Δp / Δt
What is the equation for linear momentum?
p = mv
What is the equation that relates torque to angular acceleration?
τ = mr2α
What is the gravitational constant?
G = (6.67 x 10-11 N m2 / kg2)
Describe elastic collisions. What is conserved?
The two objects that have collided bounce off of each other with no loss of energy. In real life, only subatomic particles can achieve a perfectly elastic collision, but some everyday things come pretty close (example = pool balls).
Momentum is conserved.
Kinetic energy is conserved.
