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Презентация на тему Physics 1 for KMA

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Lecture 4 Rotation of rigid bodies. Angular momentum and torque.Properties of fluids.Flotation.Bernulli equation.
Physics 1 for KMAVoronkov Vladimir Vasilyevich Lecture 4 Rotation of rigid bodies. Angular momentum and torque.Properties of fluids.Flotation.Bernulli equation. Rotation of Rigid BodiesWhen a rigid object is rotating about a fixed Radians Angular kinematicsAngular displacement:Instantaneous angular speed:Instantaneous angular acceleration: Angular and linear quantitiesEvery particle of the object moves in a circle Total linear accelerationTangential acceleration is perpendicular to the centripetal one, so the Angular velocityAngular velocity is a vector.  The right hand rule is Rotational Kinetic Energy Moment of rotational inertiaRotational kinetic energy Calculations of Moments of Inertia Uniform Thin Hoop Uniform Rigid Rod Uniform Solid Cylinder Moments of Inertia of Homogeneous Rigid Objects with Different Geometries Parallel-axis theoremSuppose the moment of inertia about an axis through the center Torque	When a force is exerted on a rigid object pivoted about an The force F has a greater rotating tendency about axis O as The force F1 tends to rotate the object counterclockwise about O, and Torque is not Force Torque is not Work	Torque should not be confused Rotational DynamicsLet’s add       which equals zero, Rotational analogue of Newton’s second lawQuantity L is an instantaneous angular momentum.The Net External Torque	The net external torque acting on a system about some Angular Momentum of a Rotating Rigid ObjectAngular momentum for each particle of Angular acceleration The Law of Angular Momentum ConservationThe total angular momentum of a system Change in internal structure of a rotating body can result in change of its angular velocity. When a rotating skater pulls his hands towards his body he spins faster. Three Laws of Conservation for an Isolated System	Full mechanical energy, linear momentum Work-Kinetic Theory for RotationsSimilarly to linear motion: The net work done by external forces in rotating a symmetric rigid Equations for Rotational and Linear Motions Gyroscope	One typical type of gyroscope is made by suspending a relatively massive At high speeds, the gyroscope exhibits extraordinary stability of balance and maintains If a gyroscope is tipped, the gimbals will try to reorient to Precession of Spinning Wheel Fluids and liquids Relative densityRelative density or specific gravity is the ratio of the density Specific volume of a substance is the ratio of the substance's volume Pressure ManometerThe difference in fluid height in a liquid column manometer is proportional to the pressure difference.P1-P2=ρgh Static Fluid PressurePstatic fluid = ρgh  where		ρ = m/V = fluid Pressure ThrustThrust is a total force in a particular direction. The unit Atmospheric PressureThe surface of the earth is at the bottom of an Atmospheric constituents Barometer Aneroid barometerAn aneroid barometeru ses a small, flexible metal box called an The Barometric Formulaμair=28.9644 g/molmair= μair/Na Pascal's PrinciplePressure exerted anywhere in a confined incompressible fluid is transmitted equally Hydraulic Press Lift pump	The lift pump, also known as a suction pump, operates as Force pump	The force pump, also known as a pressure pump, operates as Rotary PumpsRotary vane pumpScroll pump Height limitation	Total Dynamic Head (TDH) is the total equivalent height that a Total Dynamic Height	TDH = Static Height + Static Lift + Friction Loss	Static Viscosity	The resistance to flow of a fluid and the resistance to the Experimentally, under conditions of laminar flow, the force required to move a Drag force due viscosity	In a viscous fluid, a boundary layer is formed. Effect of Temperature on Viscosity 	The temperature dependence of liquid viscosity is Liquid DampingDamping is an effect that reduces the amplitude of oscillations in Buoyancy 	Buoyancy arises from the fact that fluid pressure increases with depth Archimedes' PrincipleThe buoyant force on a submerged object is equal to the Hydrometer A hydrometer is an instrument used to measure the specific gravity Determine, what liquid is denser? This liquid is lighter.This liquid is denser.This liquid is lighter. Fluid Kinetic EnergyThe kinetic energy of a moving fluid is more useful Fluid Potential EnergyThe potential energy of a moving fluid is more useful Bernoulli Equation Venturi meter	The Venturi effect is the reduction in fluid pressure that results Venturi effect	Q is volumetric flow rateSo Venturi meter can be used to measure the flow rate. Water EductorLiquid Jet Eductors use the kinetic energy of a motive liquid Torricelli’s law
Слайды презентации

Слайд 2 Lecture 4
Rotation of rigid bodies.
Angular momentum and

Lecture 4 Rotation of rigid bodies. Angular momentum and torque.Properties of fluids.Flotation.Bernulli equation.

torque.
Properties of fluids.
Flotation.
Bernulli equation.


Слайд 3 Rotation of Rigid Bodies
When a rigid object is

Rotation of Rigid BodiesWhen a rigid object is rotating about a

rotating about a fixed axis, every particle of the

object rotates through the same angle in a given time interval and has the same angular speed and the same angular acceleration. So the rotational motion of the entire rigid object as well as individual particles in the object can be described by three angles. Using these three angles we can greatly simplify the analysis of rigid-object rotation.


Слайд 4 Radians

Radians

Слайд 5 Angular kinematics
Angular displacement:

Instantaneous angular speed:


Instantaneous angular acceleration:

Angular kinematicsAngular displacement:Instantaneous angular speed:Instantaneous angular acceleration:

Слайд 6 Angular and linear quantities
Every particle of the object

Angular and linear quantitiesEvery particle of the object moves in a

moves in a circle whose center is the axis

of rotation.
Linear velocity:

Tangential acceleration:

Centripetal acceleration:

Слайд 7 Total linear acceleration
Tangential acceleration is perpendicular to the

Total linear accelerationTangential acceleration is perpendicular to the centripetal one, so

centripetal one, so the magnitude of total linear acceleration

is

Слайд 8 Angular velocity
Angular velocity is a vector.

Angular velocityAngular velocity is a vector.  The right hand rule

The right hand rule is applied: If the fingers

of your right hand curl along with the rotation your thumb will give the direction of the angular velocity.

Слайд 9 Rotational Kinetic Energy

Moment of rotational inertia

Rotational kinetic

Rotational Kinetic Energy Moment of rotational inertiaRotational kinetic energy

energy


Слайд 10 Calculations of Moments of Inertia

Calculations of Moments of Inertia

Слайд 11 Uniform Thin Hoop

Uniform Thin Hoop

Слайд 12 Uniform Rigid Rod

Uniform Rigid Rod

Слайд 13 Uniform Solid Cylinder

Uniform Solid Cylinder

Слайд 14 Moments of Inertia of Homogeneous Rigid Objects with Different

Moments of Inertia of Homogeneous Rigid Objects with Different Geometries

Geometries


Слайд 16 Parallel-axis theorem
Suppose the moment of inertia about an

Parallel-axis theoremSuppose the moment of inertia about an axis through the

axis through the center of mass of an object

is ICM. Then the moment of inertia about any axis parallel to and a distance D away from this axis is


Слайд 18 Torque
When a force is exerted on a rigid

Torque	When a force is exerted on a rigid object pivoted about

object pivoted about an axis, the object tends to

rotate about that axis. The tendency of a force to rotate an object about some axis is measured by a vector quantity called torque τ (Greek tau).



Слайд 19
The force F has a greater rotating tendency

The force F has a greater rotating tendency about axis O

about axis O as F increases and as the

moment arm d increases. The component F sinφ tends to rotate the wrench about axis O.

Слайд 20 The force F1 tends to rotate the object

The force F1 tends to rotate the object counterclockwise about O,

counterclockwise about O, and F2 tends to rotate it

clockwise.

We use the convention that the sign of the torque resulting from a force is positive if the turning tendency of the force is counterclockwise and is negative if the turning tendency is clockwise. Then

The force F1 tends to rotate the object counterclockwise about O, and F2 tends to rotate it clockwise.


Слайд 21 Torque is not Force Torque is not Work
Torque should

Torque is not Force Torque is not Work	Torque should not be

not be confused with force. Forces can cause a

change in linear motion, as described by Newton’s second law. Forces can also cause a change in rotational motion, but the effectiveness of the forces in causing this change depends on both the forces and the moment arms of the forces, in the combination that we call torque. Torque has units of force times length—newton · meters in SI units—and should be reported in these units.
Do not confuse torque and work, which have the same units but are very different concepts.

Слайд 22 Rotational Dynamics
Let’s add

Rotational DynamicsLet’s add    which equals zero, as

which equals zero, as

and are parallel.
Then: So we get




Слайд 23 Rotational analogue of Newton’s second law
Quantity L is

Rotational analogue of Newton’s second lawQuantity L is an instantaneous angular

an instantaneous angular momentum.


The torque acting on a particle

is equal to the time rate of change of the particle’s angular momentum.

Слайд 24 Net External Torque
The net external torque acting on

Net External Torque	The net external torque acting on a system about

a system about some axis passing through an origin

in an inertial frame equals the time rate of change of the total angular momentum of the system about that origin:

Слайд 25 Angular Momentum of a Rotating Rigid Object
Angular momentum

Angular Momentum of a Rotating Rigid ObjectAngular momentum for each particle

for each particle of an object:

Angular momentum for the

whole object:


Thus:

Слайд 26 Angular acceleration

Angular acceleration

Слайд 27 The Law of Angular Momentum Conservation
The total angular

The Law of Angular Momentum ConservationThe total angular momentum of a

momentum of a system is constant if the resultant

external torque acting on the system is zero, that is, if the system is isolated.


Слайд 28




Change in internal structure of a rotating body

Change in internal structure of a rotating body can result in change of its angular velocity.

can result in change of its angular velocity.


Слайд 29
When a rotating skater pulls his hands towards

When a rotating skater pulls his hands towards his body he spins faster.

his body he spins faster.


Слайд 30 Three Laws of Conservation for an Isolated System
Full

Three Laws of Conservation for an Isolated System	Full mechanical energy, linear

mechanical energy, linear momentum and angular momentum of an

isolated system remain constant.

Слайд 31 Work-Kinetic Theory for Rotations
Similarly to linear motion:

Work-Kinetic Theory for RotationsSimilarly to linear motion:

Слайд 32
The net work done by external forces in

The net work done by external forces in rotating a symmetric

rotating a symmetric rigid object about a fixed axis

equals the change in the object’s rotational energy.

Слайд 33 Equations for Rotational and Linear Motions

Equations for Rotational and Linear Motions

Слайд 34 Gyroscope
One typical type of gyroscope is made by

Gyroscope	One typical type of gyroscope is made by suspending a relatively

suspending a relatively massive rotor inside three rings called

gimbals. Mounting each of these rotors on high quality bearing surfaces insures that very little torque can be exerted on the inside rotor.

Слайд 35
At high speeds, the gyroscope exhibits extraordinary stability

At high speeds, the gyroscope exhibits extraordinary stability of balance and

of balance and maintains the direction of the high

speed rotation axis of its central rotor. The implication of the conservation of angular momentum is that the angular momentum of the rotor maintains not only its magnitude, but also its direction in space in the absence of external torque. The classic type gyroscope finds application in gyro-compasses.

Слайд 36 If a gyroscope is tipped, the gimbals will

If a gyroscope is tipped, the gimbals will try to reorient

try to reorient to keep the spin axis of

the rotor in the same direction. If released in this orientation, the gyroscope will precess in the direction shown because of the torque exerted by gravity on the gyroscope.

Слайд 37 Precession of Spinning Wheel

Precession of Spinning Wheel

Слайд 38 Fluids and liquids

Fluids and liquids

Слайд 39 Relative density
Relative density or specific gravity is the

Relative densityRelative density or specific gravity is the ratio of the

ratio of the density of a substance to the

density of a given reference material. Specific gravity usually means relative density with respect to water.



If the reference material is water then a substance with a relative density (or specific gravity) less than 1 will float in water. For example, an ice cube, with a relative density of about 0.91, will float. A substance with a relative density greater than 1 will sink.

Слайд 41 Specific volume of a substance is the ratio

Specific volume of a substance is the ratio of the substance's

of the substance's volume to its mass. It is

the reciprocal of density and is an intrinsic property of matter:


Слайд 42 Pressure

Pressure

Слайд 43 Manometer
The difference in fluid height in a liquid

ManometerThe difference in fluid height in a liquid column manometer is proportional to the pressure difference.P1-P2=ρgh

column manometer is proportional to the pressure difference.
P1-P2=ρgh


Слайд 44 Static Fluid Pressure
Pstatic fluid = ρgh where ρ

Static Fluid PressurePstatic fluid = ρgh where		ρ = m/V = fluid

= m/V = fluid density
g = gravitational acceleration
h =

depth of fluid
The pressure exerted by a static fluid depends only upon the depth of the fluid, the density of the fluid, and the acceleration of gravity

Слайд 45 Pressure Thrust
Thrust is a total force in a

Pressure ThrustThrust is a total force in a particular direction. The

particular direction. The unit of thrust, therefore is the

same as that of force: Newtons (N). Pressure is the force or thrust applied per unit area.

F=P·A

Слайд 46 Atmospheric Pressure
The surface of the earth is at

Atmospheric PressureThe surface of the earth is at the bottom of

the bottom of an atmospheric sea. The standard atmospheric

pressure is measured in various units:
1 atmosphere = 760 mmHg = 101.3 KPa
The bar is a unit of pressure defined as 100 kilopascals. It is about equal to the atmospheric pressure on Earth at sea level.
The unit mmHg is often called torr, particularly in vacuum applications: 760 mmHg = 760 torr

Слайд 47 Atmospheric constituents

Atmospheric constituents

Слайд 48 Barometer

Barometer

Слайд 49 Aneroid barometer
An aneroid barometeru ses a small, flexible

Aneroid barometerAn aneroid barometeru ses a small, flexible metal box called

metal box called an aneroid cell (capsule), which is

made from an alloy of beryllium and copper. The evacuated capsule (or usually more capsules) is prevented from collapsing by a strong spring. Small changes in external air pressure cause the cell to expand or contract. This expansion and contraction drives mechanical levers such that the tiny movements of the capsule are amplified and displayed on the face of the aneroid barometer.

Слайд 51 The Barometric Formula
μair=28.9644 g/mol

mair= μair/Na

The Barometric Formulaμair=28.9644 g/molmair= μair/Na

Слайд 52 Pascal's Principle
Pressure exerted anywhere in a confined incompressible

Pascal's PrinciplePressure exerted anywhere in a confined incompressible fluid is transmitted

fluid is transmitted equally in all directions throughout the

fluid such that the pressure ratio (initial difference) remains the same.


Слайд 54 Hydraulic Press

Hydraulic Press

Слайд 55 Lift pump
The lift pump, also known as a

Lift pump	The lift pump, also known as a suction pump, operates

suction pump, operates as follows:
on the upstroke of

the plunger, the lower valve opens, the upper valve (situated on or in the plunger itself) is closed, and the low air pressure produced in the barrel allows atmospheric pressure on the surface of the water source, down below, to make the water move up the downpipe and eventually fill the barrel below the plunger.
On the downstroke, the lower valve closes, the upper one opens, and water is forced into the barrel above the upper valve. On the next upstroke, the water above the plunger is forced out of the spout, located at the top of the barrel, at the same time as the volume below the barrel fills up with water again.

Слайд 56 Force pump
The force pump, also known as a

Force pump	The force pump, also known as a pressure pump, operates

pressure pump, operates as follows:
on the upstroke of

the plunger, the outlet or delivery valve is closed and the inlet valve opens. The low air pressure produced in the barrel causes the water below to move up the downpipe and eventually fill the barrel.
On the downstroke, the inlet valve closes, the outlet valve opens, and the water is forced out via the outlet pipe, which is located at the bottom of the barrel.

Слайд 57 Rotary Pumps
Rotary vane pump
Scroll pump

Rotary PumpsRotary vane pumpScroll pump

Слайд 58 Height limitation
Total Dynamic Head (TDH) is the total

Height limitation	Total Dynamic Head (TDH) is the total equivalent height that

equivalent height that a fluid is to be pumped,

taking into account friction losses in the pipe.

Слайд 59 Total Dynamic Height
TDH = Static Height + Static

Total Dynamic Height	TDH = Static Height + Static Lift + Friction

Lift + Friction Loss
Static Height is the maximum height

reached by the pipe after the pump (also known as the 'discharge head').
Static Lift is the height the water will rise before arriving at the pump (also known as the suction head).
Friction Loss - in any real moving fluid, energy is dissipated due to friction; turbulence dissipates even more energy for high Reynolds number flows. Friction loss is divided into two main categories, "major losses" associated with energy loss per length of pipe, and "minor losses" associated with bends, fittings, valves, etc.

Слайд 60 Viscosity
The resistance to flow of a fluid and

Viscosity	The resistance to flow of a fluid and the resistance to

the resistance to the movement of an object through

a fluid are usually stated in terms of the viscosity of the fluid.

Слайд 61
Experimentally, under conditions of laminar flow, the force

Experimentally, under conditions of laminar flow, the force required to move

required to move a plate at constant speed against

the resistance of a fluid is proportional to the area of the plate and to the velocity gradient perpendicular to the plate. The constant of proportionality is called the viscosity .

Слайд 63 Drag force due viscosity
In a viscous fluid, a

Drag force due viscosity	In a viscous fluid, a boundary layer is

boundary layer is formed. This causes a net drag

due to skin friction. Further, because the ideal pressure now acts on the boundary layer, as opposed to the ship, and the boundary layer grows along the length of the ship, the net opposing forces are greater than the net supporting forces. This further adds to the resistance.

Слайд 64 Effect of Temperature on Viscosity
The temperature dependence

Effect of Temperature on Viscosity 	The temperature dependence of liquid viscosity

of liquid viscosity is the phenomenon by which liquid

viscosity tends to decrease (or, alternatively, its fluidity tends to increase) as its temperature increases.

here η0 and b are constants.
This is an empirical model that usually works for a limited range of temperatures.


Слайд 65 Liquid Damping
Damping is an effect that reduces the

Liquid DampingDamping is an effect that reduces the amplitude of oscillations

amplitude of oscillations in an oscillatory system
Fluid viscous damping

is a way to add energy dissipation to the lateral system of a building structure. A fluid viscous damper dissipates energy by pushing fluid through an orifice, producing a damping pressure which creates a force. These damping forces are 90 degrees out of phase with the displacement driven forces in the structure. This means that the damping force does not significantly increase the seismic loads for a comparable degree of structural deformation.

Слайд 68 Buoyancy
Buoyancy arises from the fact that fluid pressure

Buoyancy 	Buoyancy arises from the fact that fluid pressure increases with

increases with depth and from the fact that the

increased pressure is exerted in all directions (Pascal's principle) so that there is an unbalanced upward force on the bottom of a submerged object.

Слайд 69 Archimedes' Principle
The buoyant force on a submerged object

Archimedes' PrincipleThe buoyant force on a submerged object is equal to

is equal to the weight of the fluid displaced.


The upward thrust which the surrounding fluid exerts on an object is referred to as the force of buoyancy.


Слайд 70 Hydrometer

A hydrometer is an instrument used to

Hydrometer A hydrometer is an instrument used to measure the specific

measure the specific gravity (or relative density) of liquids;

that is, the ratio of the density of the liquid to the density of water.
A hydrometer is usually made of glass and consists of a cylindrical stem and a bulb weighted with mercury or lead shot to make it float upright. The liquid to be tested is poured into a tall container, often a graduated cylinder, and the hydrometer is gently lowered into the liquid until it floats freely. The point at which the surface of the liquid touches the stem of the hydrometer is noted. Hydrometers usually contain a scale inside the stem, so that the specific gravity can be read directly. A variety of scales exist, and are used depending on the context.
Hydrometers may be calibrated for different uses, such as a lactometer for measuring the density (creaminess) of milk, a saccharometer for measuring the density of sugar in a liquid, or an alcoholometer for measuring higher levels of alcohol in spirits.

Слайд 72
Determine, what liquid is denser?

Determine, what liquid is denser?

Слайд 73 This liquid is lighter.
This liquid is denser.
This liquid

This liquid is lighter.This liquid is denser.This liquid is lighter.

is lighter.


Слайд 74 Fluid Kinetic Energy
The kinetic energy of a moving

Fluid Kinetic EnergyThe kinetic energy of a moving fluid is more

fluid is more useful in applications like the Bernoulli

equation when it is expressed as kinetic energy per unit volume


Слайд 75 Fluid Potential Energy
The potential energy of a moving

Fluid Potential EnergyThe potential energy of a moving fluid is more

fluid is more useful in applications like the Bernoulli

equation when is expressed as potential energy per unit volume



Слайд 76 Bernoulli Equation

Bernoulli Equation

Слайд 77 Venturi meter
The Venturi effect is the reduction in

Venturi meter	The Venturi effect is the reduction in fluid pressure that

fluid pressure that results when a fluid flows through

a constricted section of pipe.
The Venturi effect is named after Giovanni Battista Venturi (1746–1822), an Italian physicist.

Слайд 78 Venturi effect
Q is volumetric flow rate
So Venturi meter

Venturi effect	Q is volumetric flow rateSo Venturi meter can be used to measure the flow rate.

can be used to measure the flow rate.


Слайд 79 Water Eductor
Liquid Jet Eductors use the kinetic energy

Water EductorLiquid Jet Eductors use the kinetic energy of a motive

of a motive liquid to entrain another liquid, completely

mix the two, and then discharge the mixture against a counter pressure and are used for pumping and mixing operations.

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