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Final

# Physics Final Review.docx

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University of Guelph

Physics

PHYS 1080

Mike Massa

Fall

Description

Physics Final Review:
Mechanics:
- Relationship between object’s motion (kinematics) and forces acting on it (newton’s
laws)
Displacement: velocity: acceleration:
If a=0: v=v ond x=x + vot o
- Displacement is
- displacement is positive
- Velocity is positive and positive
constant - Velocity is increasing
- Acceleration is positive
- Acceleration is zero
- Displacement is positive - Displacement is positive
- Velocity is increasing
- Velocity is positive and
constant - Acceleration is positive
- Acceleration is zero
- Area under curve =
displacement
Gravity influences motion with constant vertical acceleration g= 9.8m/s , motion in the
horizontal and vertical direction are independent of each other
Pen swipe: swipe over θ gives cos, away gives sin; put pen over vector r and then rotate it from
there to component of interest
Relative velocity:
- Motion occurs at constant velocity but total motion is due to contribution from 2 factors
- Ex. Someone trying to swim directly across a river with a current
- Usually contain 3 velocities: identify 2 and add to determine 3 (resultant)
- Wind speed or water speed not likely resultant velocity
- One velocity in normal conditions
- Combine to give resultant or net motion
Force:
- Interaction between 2 bodies: an object and an agent
- Something that causes an acceleration
- A vector (magnitude and direction)
- Without a force there is no acceleration
1 - Can be produced with or without contact
- Types: gravitational, normal force, tension, friction, magnetic/electric
Newton’s laws of motion:
- An object in a state of uniform motion will remain doing so unless acted on by a non-zero
resultant force
- If a resultant force acting on an object leads to an acceleration in the direction of the
force, the acceleration is proportional to the force and inversely proportional to the
object’s mass
- For every force there is an equal but opposite reaction force
⃗⃗⃗⃗⃗⃗⃗ object at rest remains at rest and object in motion remains in motion unless
external force is applied
Static equilibrium- net force is zero and object isn’t moving (v=0)
Dynamic equilibrium- net force is zero and object moves with constant velocity
Equilibrium ⃗⃗⃗⃗⃗⃗⃗
Free body diagrams- diagram that represents all forces acting on object
- Don’t draw forces acting on other objects, caused by this object, internal forces, forces
for “ma” term
Static friction (objects that are NOT moving):
- fswill match applied force
- f doesn’t have a pre-defined value
s
- force of static friction can have value up to some maximum (just as object starts to move)
- static friction will take whatever value is needed to ensure that the object obeys Newton’s
Laws
Kinetic friction (unbalanced forces):
- fk=µ k
- when drawing FBD line up x or y axis with direction of acceleration
Torque- forces caused by rotation
- measure of ability of a force to cause rotation of an object
- depends on how hard we push (F), how far we are from pivot (R)
2 - generate a larger torque with either a larger force or by applying force at a larger distance
from pivot
- in order to keep things from rotating, applied torques must satisfy:
Linear momentum: [kg•m/s]
Conservation of momentum:
- system with no external forces, total momentum remains constant
- comes from Newton’s laws of motion
- remember: total comes from a vector summation over all objects in system
Momentum in 2-D:
- is a vector quantity- can treat x,y components independently, conservation of
momentum applies to each
- Collision types: completely inelastic objects stick together, elastic energy is
conserved
Energy and work:
- Kinetic
- Gravitational potential
- Food/chemical
- Heat
2 2
- Units: Joule= kg•m /s
- Work= force x distance
- Work and energy are both scalar
Work done by a conservative force is independent of path traveled by object the force is acting
on; same no matter the path
Work done by non-conservative force depends on path taken
Kinetic and potential energy: K= ½ mv 2
Change in K = total work done on object:
Potential Energy (gravity): U=mgy
When height changes, you have a change in potential energy ** only the vertical displacement
matters: ΔU=mgΔy
3 Conservation of energy:
- Energy can be transferred from one form to another but the total energy of the system is
conserved
- E= Total mechanical energy
- With only conservative forces (gravity, elasticity) only
initial and final positions matter
- When work is done on the system work done by friction depends on objects path
Uniform Circular Motion:
- Object moves in a circular motion at a uniform speed,
the velocity is tangent to the circle
- Must be an acceleration that has direction towards
center of circular path
Period (T)- time to travel circumference
Frequency f=1/T
Radians- units of measure of angular distance in θ direction 2π radians= 360⁰
Angular velocity (ω): ω=2π/T = 2πf
Centripetal acceleration: v=rω, so a second expression for centripetal acceleration is:
Centripetal force- force directed radially inward on an object moving in a circular path, source
of centripetal force could be gravity, tension, friction, etc.
RESULTANT FORCE
- Don’t add as a contributing force in FBD
Centrifugal force- radially outward from axis of rotation, a fictitious
force arising from observations from a non-inertial frame of reference
Position described by angle θ, distance displacement:
Units:
2
Angular velocity (ω): [rad/s] Angular acceleration (α): [rad/s ]
Convention: define positive direction to be counter clockwise
4 The effectiveness of force at causing rotation depends on:
- Magnitude of force
- Distance from pivot
- Direction of force with respect to pivot
The net torque acting on a system is the vector sum of all torques action on the system
Rigid body equilibrium:
Translational equilibrium:
Rotational Equilibrium:
Therefore a rigid body is in equilibrium if both
Force of gravity acts at centre of mass- for objects of uniform density, simple shape, and centre
of mass is at centre of object
Using a pivot point- choose based on simplifying problem (fewer torques to consider)- forces
point directly towards/away from pivot, forces acting at zero distance from pivot
**for statics can choose pivot anywhere you want and can look at as many pivots as it takes
Two ways to think about torque:
The lever arm or momentum arm is perpendicular distance from the
axis of rotation to the line of the force
θ is the angle between force and line from pivot to point of force
Rotational Kinetic Energy:
Moment of inertia:
- Depends on rotation axis
- m far from axis large I
- m close to axis small I
- for some extended body rigid objects there is often a simple expression for I such as:
5 Kinetic energy- of a spinning top- rotation axis is fixed:
Kinetic energy of a flying frisbee (rotational and translational):
For rolling need friction
Disc vs. hoop: small I large v, small I in ½ Iω term means more of
the input energy, mgh, can be used to increase v
6 If there is a net torque, the object will rotationally accelerate:
⃗
Conservation of angular momentum (L): , if no external torque is applied then
angular momentum is conserved (L=constant)
When you can’t use conservation of angular
momentum:
- when the external force is applied to the system, the system’s
momentum, p is no longer conserved
- when an external torque is applied to a system, the system’s
angular momentum is no longer conserved
Elasticity- no material is completely rigid: apply a force, it will
deform, depending on type of material, some things may deform
more readily than others, apply large enough force, eventually it will
break
Ways to deform: tension, compression, shear, torsion
Tension and compression: Y= Young’s modulus [N/m =Pa] 2
2
Stress (σ) [N/m ]
Strain (ε) [no units]
Linear regime: when deformations are small Y is constant (but
Y[tension] and Y[compression] may be different)
Shear Deformation: G= shear modulus [N/m =Pa] 2
Non-linear response to stress (human bones): tension and compression applied at same time;
starts off linear
Torsional shear for a solid cylinder: torsional shear for a hollow cylinder:
Scaling: set of arguments that can be used to suggest reasons behind some trends in living
organisms such as upper limits to size, function of organs, strength, speed, intelligence, age
Isometric= same geometry, different size
When we compare 2 objects we assume that their linear dimensions (length, width, height) scale
in same proportion
7 Use ratios: Define a length scale L, Area (heat flow, strength) ∝ L ; volume (mass, heat
generation) ∝L 3
Fluid statics:
- molecular motion of fluids atoms/molecules collide with container walls- results in
force on walls
Pressure- magnitude of normal force per unit area; same2in every direction, liquid exerts
this pressure on any immersed surface; Units: N/m = Pa, atm=101.3 kPa
Hydrostatic pressure- pressure in a fluid that depends on the depth; deeper greater P
ΔP ρgh
Absolute vs. Gauge pressure:
- Atmospheric pressure around us is an absolute pressure
- Gauge pressure is a measure of one absolute pressure relative to another absolute
pressure
- Reference pressure (P ) 1ypically the atmosphere so:
- Gauge can be negative
- U-tube manometers are used to measure pressure differences between 2 gas
chambers
Other units of pressure: mmHg, bar, cmH O 2
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