PHL232H1 Lecture Notes - If And Only If

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purplezebra711

2 Nov 2011

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Couterfactual conditional: conditional whose truth is not guaranteed by the falsity of the antecedent [or the truth of the consequent: conditionals where a is false in the actual world. Involve not just the way things are, but the way things could be. The basic properties of relations ** question on exam: a relation is what is expressed by a 2-place predicate, ex. X loves y, x is taller than y, x got here before y did. Sibling and being in the same room as someone. If someone is your sibling, then they are your sibling. If someone is in the same room as you, you are in the same room as them. Being to the left of someone is not symmetric: reflexive: iff for all x in the domain. Being the same height as himself and everything is identical with itself. You will always bare your height to yourself.

Related Questions

1) A carnival clown rides a motorcycle down a ramp and around avertical loop. If the loop has a radius of 18 m, what is theslowest speed the rider can have at the top of the loop to avoidfalling?
Hint: At this slowest speed, the track exerts no force on themotorcycle at the top of the loop.

2) An airplane flies at 200.0 km/h relative to the air. What is thevelocity of the plane relative to the ground if it flies during thefollowing wind conditions?
a. a 50.0-km/h tailwind
b. a 50.0-km/h headwind.

I just need help how to start the problem because I get how to dothe work and everything, I just don't get the "physics" in thequestion.

A coin rests 15.0 cm from the center of a turntable. The coefficient of static friction between the coin and turntable surface is 0.350. The turntable starts from rest at t = 0 and rotates with a constant angular acceleration of 0.730 rad/s².

(a) Once the turntable starts to rotate, what force causes the centripetal acceleration when the coin is stationary relative to the turntable? Under what conditions does the coin begin to move relative to the turntable?

(b) After what period of time will the coin start to slip on the turntable?

bronzezebra978

Learning Goal: Understand how to determine the constants in thegeneral equation for simple harmonic motion, in terms of giveninitial conditions.
A common problem in physics is to match the particular initialconditions - generally given as an initial position x_0 andvelocity v_) at t=0 - once you have obtained the general solution.You have dealt with this problem in kinematics, where theformula

1. x(t) = x_0 + v_0t + at^2

has two arbitrary constants (technically constants of integrationthat arise when finding the position given that the acceleration isa constant). The constants in this case are the initial positionand velocity, so "fitting" the general solution to the initialconditions is very simple.

For simple harmonic motion, it is more difficult to fit the initialconditions, which we take to be

x_0, the position of the oscillator at t = 0, and
v_0, the velocity of the oscillator at t = 0.

There are two common forms for the general solution for theposition of a harmonic oscillator as a function of time t:

2. x(t) = A\cos(omega t + phi) and
3. x(t) = C\cos(omega t) + S\sin(omega t),

where A, phi, C, and S are constants, omega is the oscillationfrequency, and t is time.

Although both expressions have two arbitrary constants--parametersthat can be adjusted to fit the solution to the initialconditions--Equation 3 is much easier to use to accommodate x_0 andv_0. (Equation 2 would be appropriate if the initial conditionswere specified as the total energy and the time of the first zerocrossing, for example.)

Find C and S in terms of the initial position and velocity of theoscillator.
Give your answers in terms of x_0, v_0, and omega. Separate youranswers with a comma.

PHL232H1 Lecture Notes - If And Only If

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