Physics Exam 3 2
Terms
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- angular displacement
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-angle through which a rigid object rotates about a fixed axis
-counterclockwise = postive
-clockwise = negative - Revolution
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-one complete turn of 360 degrees
-1 rev = 2(pie) rad - uniform circular motion
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-constant tangential speed which is magnitude of tangential velocity
-tangential quantities describe motion of single point on object - Torque
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-net external torque causes the rotational velocity to change
-greater torque causes greater angular acceleration
-positive: F produces counterclockwise rotation about axis - Rigid Objects in Equilibrium
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-neither translational (linear) nor rotational motion changes
-translational and angular acceleration are zero
F = 0 and t = 0 - Center of Gravity
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-point on rigid object at which its weight can be considered to act when the torque due to w is being considered
-symmetric object with uniform weight has cg at geometerical center - Center of Gravity for a group of objects
- -change in weight distribution of a group causes a change in position of cg which if too great results in the group not remaining in equilibrium
- Moment of Inertia
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-further particle is from axis of rotation, greater the contribution to inertia
-rigid body does not have an unique moment of inertia - Ideal Spring
- -for small displacements, force applied required to stretch or compress a spring is directly proportional to the displacement x
- Spring Constant (k)
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-stiffness of spring
-large k means the spring is stiff in that a large F is required to stretch or compress it
-k is inversely proportional to the number of coils in the spring (shorter springs are stiffer springs) - Reaction Force
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-restoring force
-applied to the object the spring is attached to
-always points in a direction opposite to the displacement of the spring and leads to a back-and-forth motion of the object - Simple Harmonic Motion
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-when restoring force has equation F = -kx
-when move one revolution or cycle around reference circle execute one cycle of back-and-forth motion - Amplitude (A)
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-maximum excursion from equilibrium
-radius A is amplitude in reference circle
-constant in SHM because no mechanism for dissipating energry - Period (T)
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-time required to complete one cycle
-depends on w
-shorter w = shorter time to complete one revoluion - Velocity
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-not constant (varies bwt max and min values)
-zero when change direction at either end of oscillatory motion
-max when x = 0 (midpoint) - Acceleration
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-must have accerleration since velocity is changing
-max acceleration occurs when displacement is greatest because the force acting on the object is a maximum - Frequency of vibration
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-assuming mass of spring is negligible, only force acting on object in horizontal direction is due to spring (restoring force)
-mass increases, frequency of simple harmonic motion increases - Elastic Potentional Energy
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-due to elastic PE a stretched or compressed spring can do work on an object that is attached to the spring
-when a door is opened, a spring inside the unit is compressed and has elastic PE
-when the door is released, the compressed spring expands and does the work of closing the door (uses stored elastic PE) - Values of Elastic PE
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-max for a fully stretched or compressed spring
-zero for a spring that is neither compressed nor stretched - Simple Harmonic Motion and Two-Box System: maximum speed
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-max speed at x = 0 (object is passing through point where spring is unstrained
-max speed of two-box system is same as one box since second box is attached at x = 0 and has same speed - SHM and Two-Box system: Kinetic Energy
- -at the same speed, the KE of the two box system is twice that of the singel box system since the mass is twice
- SHM and 2 box system: Elastic Potential Energy
- -since have twice KE, will have twice the elastic PE when comes to halt
- SHM and 2 box system: Amplitude
- -two box system has greater amplitude by factor of square root of 2
- SHM and 2 box system: angular frequency
- -two box system has smaller angular frequency by a factor of square root of 2
- Simple Pendulum
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-gravity is responsible for back and forth rotation
-rotation speeds up as the particle approaches lowest point on arc and slows down on upward part of swing
-net torque is required to change angular speed
-small angular displacement then swinging is approx SHM - Physical Pendulum
- -moment of ineria is proper value for rigid object
- Damped Harmonic Motion
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-decrease in amplitude
-presence of energy dissipation
-as increase degree of damping, fewer oscillations - Damping and cars
- -shock absorber is designed to introduce a damping force which reduces the vibration associated with a bumpy ride
- Critical Damping
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-smallest degree of damping that completely eliminates the oscillation (settle back to equilibrium)
-motion is said to be critically damped
-when above value, takes longest time to return to equilibrium - Driven Harmonic Motion
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-amplitude increases
-energy is added to oscillating system
-additional force added is driving force (controls behavior - Resonance
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-large amplitude motion even if relatively weak force
-occurs when frequency of driving force matches a frequency at which the object naturally vibrates
- - Young's modulus
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material with greater Y undergoes smaller change in length
-refers to change in length of one dimension of a solid object as a result of tensile or compressive force - Tensile Force
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perpendicular to surface whose area is A
-elastic deformation - shear force
- parallel to surface whose area is A
- Shear modulus
- refers to change in shape of a solid object as a result of shearing force