## Forces, circular motion, and gravitation

##### Created by:

taewon990  on March 29, 2012

##### Description:

BR physics chapter 2

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# Forces, circular motion, and gravitation

 Newton's first law of motionAn object at rest will remain at rest, and an object in motion will continue to move with uniform velocity in a straight line, unless acted upon by an external force.
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#### Definitions

Newton's first law of motion An object at rest will remain at rest, and an object in motion will continue to move with uniform velocity in a straight line, unless acted upon by an external force.
Newton's second law of motion A force acting on an object will give that object an acceleration in the direction of the force, the acceleration of the object is directly proportional to he resultant force applied to he object and inversely proportional to the mass of the object. F = ma
Newton's third law of motion If one object exerts a force on a second object, the second object will exert a reaction force on the first object which is equal in magnitude, but opposite in direction.
How to handle formula identification poblems Check the units in the formula to make sure everything cancels. Plug in numbers like 0 or 1 and predict how the system, represented by the formula, would behave to eliminate any choices that doesn't make sense conceptually.
Which equation represents the acceleration of a package sliding down a frictionless inclined plane that makes an angle θ with the horizontal ground? Which equation represents the force a package that is canceled out by the normal force? Visualize the figure first. a= F / m
a = mg sinθ / m
a = g sinθ

N = mg cosθ
Newton's Law of Gravitation F = G M1M2 / r²
How do you determine your weight in a system that was accelerating? What would happen if the system was free-falling? What would happen if the system was accelerating with the same magnitude but in opposite direction of gravity? weight = (1 + a/g); this gives you the FACTOR you multiply the weight with.
when free-falling, weight = (1 - g/g); you weigh 0
when accelerating upward with magnitude of g, weight = (1 + g/g), so you 2x the weight.
What is the connection between arc length (S), radius (r), and angle (θ) for motion in a circle? S = θ r (θ measured in radians)
how do you convert radians into degrees and vice versa?
θ radians = θ degrees (pi / 180 degrees)
θ degrees = θ radians (180 degrees / pi)
1 rad = 57.3 degrees (from 360 degrees / 2π)
What formula(s) can be used to represent angular velocity? Δθ / Δt = ΔS/r * Δt
Δθ / Δt = v / r
ω = Δθ / Δt
ω = v / r
What formula(s) can be used to represent angular acceleration? Δω / Δt = Δv/r * Δt
Δω / Δt = a / r
α = a / r
What formula(s) can be used to represent centripetal acceleration?In a circle, Δθ = S / r
when considering acceleration, Δθ = Δv/v, where Δv is the arc length and v is the radius. Divide both sides by Δt to get: Δθ / Δt = Δv/v * Δt
this equals to: ω = a / v
plug in v / r for ω to get:
centripetal acceleration = v²/ r
plug in ωr for v to get:
centripetal acceleration = ω²/ r
A centrifuge at 1500 rpm is later turned off by decelerating at 16 rev / min². How long will it take to stop spinning? 11minutes
use ω = ωo + αt
As you start walking towards the center of a merry-go-round, what happens to the acceleration? Consider the two equations
centripetal acceleration = v²/ r
centripetal acceleration = ω²/ r

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