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P6 - (Prelims)
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Gravity
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Key Concepts:
Terms in this set (152)
ROTATION
refers to the motion of a body turning about an axis, where each particle of the body moves along a circular path.
angular quantities
Physicists use _____ to describe rotation.
GREEK LETTERS
used to represent angular quantities.
ANGULAR POSITION
θ
ANGULAR VELOCITY
defined in analogy with linear velocity.
ANGULAR VELOCITY
Represented by ω
ANGULAR VELOCITY
Rate at which angular displacement changes with time.
LINEAR VELOCITY
s/t
ANGULAR ACCELERATION
the time rate of change of angular velocity.
MOMENT OF INERTIA
also known as rotational inertia
MOMENT OF INERTIA
Is the rotational analog for mass and is represented by a capital letter I.
MOMENT OF INERTIA
The property of a rotating body to resist change in its state of rotation
MOMENT OF INERTIA
The larger the _____, the greater the resistance it offers to angular acceleration.
MOMENT OF INERTIA
SI unit is kg∙m^2
RADIUS OF GYRATION
the distance from an axis of rotation where the mass of a body may be assumed to be concentrated without altering
RADIUS OF GYRATION
(k) in rotation
Global warming
involves the rising of the average temperature of the atmosphere near Earth's surface.
climate change.
One effect of global warming is _____
FELIX LANDERER
at the Max Planck Institute for Meteorology in Hamburg, Germany, the water mass will shift away from the equator toward the poles. This will result in a decrease in Earth's moment of inertia and a corresponding increase in its angular velocity. It is further predicted that the day will be 0.12 millisecond shorter two centuries from now.
RICHARD RAY
geophysicist at NASA Goddard Space Flight Center said, "So it would partly cancel out this effect."
PARALLEL AXES THEOREM
the moment of inertia I at any axis is equal to the moment of inertia I_c about a parallel axis passing through the center of mass and the product of the body and the square of the perpendicular I=I_c+m〖r_⊥〗^2
TORQUE
effectiveness of a force in rotating a body on which it starts
TORQUE
Moment of force
TORQUE
Greek letter tau (τ)
Rotation
_____is greatest when force is applied perpendicularly to the door.
90°
Maximum torque can be obtained if θ is
Positive
counterclockwise
Negative
clockwise
First law of motion
states that a body at rest will not rotate nor will a rotating body change its angular velocity unless acted upon by an external unbalanced torque
Second law of motion
states that an unbalanced torque acting on a rigid body produce angular acceleration.
angular acceleration
is directly proportional to and in the same direction as the unbalanced torque τ and inversely proportional to the body's moment of inertia I about the axis of rotation.
Second law of motion
τ=Iα
Third law of motion
applied to rotation states that to every action torque, there is an equal but opposite reaction torque.
Human spinal column
is made up of 24 vertebrae separated by fluid-filled disks.
lumbosacral disk
The disk separating the last vertebrae from the bone supporting the spine is called the _____
Sacrum
the bone supporting the spinal column
Spinal column
acts as the lever while the sacrum acts as the fulcrum when one bends over.
ANGULAR MOMENTUM
product of its moment of inertia (I) about this axis and its angular velocity ω
ANGULAR MOMENTUM
L=Iω
ANGULAR MOMENTUM
kg∙m^2/s
conserved
In the absence of a net external torque, the total angular momentum of a system is _____.
Work
____ in rotation is the product of torque and angular displacement. Power is work done divided by time.
Work
W=τθ
Power
P=W/t
kinetic energy
of a rotating rigid body (K_R)is K_R=1/2 Iω^2
...
...
total kinetic energy
For a rolling body, the _____ (K_T) the sum of its translational kinetic energy (K) and rotational kinetic energy (K_R)
STATICS
Concerned with the calculation of forces acting on and with structures that are in equilibrium.
Archimedes
introduced the concept of lever equilibrium as early as 287-212 BC.
Leonardo da Vinci
conceptualized moments in relation to equilibrium in the latter part of the fifteenth century.
CENTER OF GRAVITY
is a useful concept when dealing with equilibrium problems.
CENTER OF GRAVITY
The point where its entire weight may be assumed to be concentrated.
CENTER OF GRAVITY
are identical on the assumption that the body is small enough for g not to vary over its extent.
CENTER OF GRAVITY
May be inside or outside of the body.
CENTER OF GRAVITY
For regular-shaped object, the ___ is its geometric center.
CENTER OF GRAVITY
For irregular shaped object, the ___ may be determined experimentally, either by balancing or using the plumb line method.
Condition of stability
an object will be stable if a plumb line drawn from its center of gravity falls within its base.
Translational equilibrium
object that has no net force on it
Translational equilibrium
∑▒F=0 Eq.(7.17)
Rotational equilibrium
necessary condition for a body
Rotational equilibrium
∑▒τ=0 Eq. (7.19)
Rotational equilibrium
Second law for equilibrium
Equilibrant
if the resultant of the forces acting on a body is not zero, the addition of another force is needed to balance the resultant to produce translational equilibrium.
Particle
may be considered as a point mass
Point mass
Force acting on ___ are concurrent and hence there is no concern for rotation. Only the first condition of equilibrium must be satisfied due to the absence of force/s that would cause rotation (torque)
Rigid body
extended body in space that does not change its size and shape.
rigid body
Most often, the lines of action of the forces acting on a ___ do not pass through a common point. Hence, it may be set into rotation although the vector sum of the forces may be equal to zero.
rigid body
for a ___ to be in equilibrium, the two conditions must be satisfied.
LESSON 7.3 MOTION OF HEAVENLY BODIES
...
Tycho Brahe
recorded accurate measurements of the motion of planets around the sun.
Johannes Kepler
after painstakingly analyzing and studying these measurements for 22 years, formulated his three laws of planetary motion.
Isaac Newton
discovered the physical law that governs an apple falling from the tree to the ground.
LAW OF ELLIPSES
The orbit of a planet around the sun is an ellipse with the sun at one focus.
LAW OF EQUAL AREAS
The planet moves around the sun in such a way that a line drawn from the sun to the planet sweeps out equal areas in equal intervals of time.
Perihelion
- fastest (shortest distance)
Aphelion
- slowest (farthest distance)
HARMONIC LAW OR THE LAW OF PERIODS
It states that the ratio of the squares of the periods T of any two planets revolving around the sun is equal to the ratio of the cubes of their mean distances d from the sun.
Period
is the time for a planet to travel one revolution around the sun.
Johannes Kepler -
a religious man, making reference to God in all his writings. He believed that God created the universe according to a mathematical plan. He introduced the word "satellite" (literally means attendant) to refer to the moons orbiting Jupiter.
Kepler's conjecture
hexagonal closed pack and cubic closed pack in solid state physics.
Johannes Kepler
Proved that multiplication and division may be reduced to simple addition and subtraction using logarithms.
Astronomical unit
A convenient unit of measurement for period is Earth year or simply year
Astronomical unit
A unit of distance from the sun is called Astronomical unit (AU)
AU
is the average separation of Earth from the sun.
Gravitation
- universal attraction (proposed by Newton)
Gravitation
Happens between all bodies by virtue of their masses.
law of universal gravitation
states that every object in the universe attracts every other object with a force proportional to the product of their masses,
Acceleration due to gravity
- The acceleration due to gravity at a particular distance r from the center of a planet of mass M can be determined using Newton's second law of motion and law of universal gravitation.
Satellite
- any object that orbits a planet or a star.
Satellite
May be natural or artificial.
Satellite
Orbit is nearly circular. Centripetal force is needed to keep this satellite moving in a circle.
Centripetal force
is provided by the force of attraction between the satellite and the planet it orbits.
SYNCOM
- is a short term for synchronous communication satellites
SYNCOM
A satellite having the same period of revolution to the period of rotation of the planet it orbits.
SYNCOM
The satellite also completes one revolution in 24 hours.
SATELLITE DISHES
-Stationary antennas that are placed in our homes receive signals without changing orientations from a revolving satellite.
GRAVITATIONAL POTENTIAL ENERGY
- defined as the work needed to move an object from an initial position to final position.
Negative work
is done to bring an object closer to Earth.
negative
when using infinity as the reference point, gravitational potential energy is always ___.
ESCAPE VELOCITY
defined to be the minimum velocity an object must have in order to escape its gravitational field without ever falling back.
conjunction
The heavens smiled down on Earth last December 1, 2008. Jupiter and Venus aligned- an event known as a ____ - and were joined by a thin sliver of moo.
Diwata
- is the first microsatellite designed and assembled by an all- Filipino team from the University of the Philippines Diliman and the Department of Science and Technology Advanced Science and Technology Institute under the supervision of Japanese scientists from Hokkaido University and Tohoku University.
Diwata
One of the microsatellites to be built under the Philippine Scientific Earth Observation Microsatellite (PHL-Microsat) Program.
Diwata
50 kg was finally completed and handed to Japan Aerospace and Exploration Agency for final testing.
Diwata
It was launched from the National Aeronautics and Space Administration Camp Canaveral Florida, USA to the International Space Station last March 23, 2016. On April 27, 2016, it was deployed to start its mission
LESSON 8.1 PERIODIC MOTION
...
Periodic Motion
- refers to motion that is repeated at regular intervals of time.
Equilibrium position
- also known as resting position
Equilibrium position
The position assumed by the body when it is not vibrating.
Restoring force
- is a force that tends to restore a body from its displacement to its equilibrium position
Amplitude
- the maximum displacement of a body from its equilibrium position.
Period
- the time required to make a complete to-and-fro motion.
Period
-usually expressed in seconds
Cycle
- one complete to-and-fro
Frequency
the number of cycles per unit of time.
Frequency
SI unit is hertz (Hz)
hertz
One ____ is equal to one cycle per second.
Frequency
Reciprocal of period
Angular frequency
used instead of frequency.
Angular frequency
Expressed in radians per second
SIMPLE HARMONIC MOTION
Type of periodic motion where the restoring force is proportional to the displacement of the body from its equilibrium position. This restoring force acts in a direction opposite that of the displacement.
x
is the displacement from equilibrium position
k
is a proportionality constant
negative sign
simply means that the restoring force and displacement are oppositely directed.
SIMPLE HARMONIC OSCILLATORS
- systems exhibiting simple harmonic motion
Mass-spring system
The simplest form of a simple harmonic oscillator is a body of mass m oscillating on one end of an elastic spring
mechanical energy
Total ____ will remain constant as long as there is no friction.
maximum displacement
When an object is at its ____ (amplitude), its velocity, and hence the kinetic energy, is zero. In this case, displacement x is replaced by amplitude A. The total energy will then beE=1/2 kA^2
maximum speed
The speed v of this body is the circumference of the circle divided by time. The ____ is obtained when the radius of the circle is equal to the amplitude.
maximum speed
v_max= 2πA/T Eq. (8.9)
Simple harmonic motion
- a projection of uniform circular motion along a diameter.
CHRISTIAAN HUYGENS
- invented the grandfather's clock in 1658. Before its invention, time keeping devices were only accurate to about 15 min a day. However, the grandfather's clock reduced the error to about 15 s a day.
grandfather's clock
The ____ was originally called floor clock or pendulum clock.
Henry Clay Work
Got its name from a song written in 1875 by ___ entitled "Grandfather's Clock"
PENDULUM
- Any object which can swing freely from a pivot point under the influence of gravity.
PENDULUM
-may be simple or physical
SIMPLE PENDULUM
- Consists of a concentrated mass called the bob suspended by a light thread and attached to a fixed support
Restoring force
F=mgsinθ
simple harmonic
For motion to be____ , the restoring force must be proportional to s or to θ since s=θL
angular displacement
If the ____ is small, the arc s is almost horizontal and may be assumed to be equal to x and sinθ is almost equal to θ in radians.
directly proportional
The period of a simple pendulum is ____ to the square root of its length
inversely proportional
The period is ___ to square root of the acceleration due to gravity
independent
The period is ___ of the mass of the bob
independent
The period is ____ of the angular amplitude if angular displacement is small, say less than or equal to 10 °
Physical pendulum
- one where the hanging object is a rigid body.
Damped harmonic oscillation
- An object initially set into vibration will have its amplitude continuously decreasing due to frictional effects. Eventually, the object will stop moving.
UNDERDAMPED OSCILLATION
- the system oscillated with decreasing amplitude until it becomes zero.
CRITICAL DAMPED SYSTEM
- returns to equilibrium faster than overdamped system.
Underdamped and critical
- return to equilibrium without oscillating
FORCED VIBRATION
- every simple harmonic oscillator has its natural frequency. However, if such system is subjected to an external force
RESONANCE
- the frequency of force matches the natural frequency of the vibrating system
Enrico Caruso
Shattering of wine goblet by operatic tenor ____ while singing and collapsing of buildings and other structures during earthquakes are some of the effects of resonance.
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