Physical quantities, Units and Vectors Flashcards
100% mastery in the concepts
systematic error
errors as a result of the experimenting instrument
random error
errors as a result of the lapses in skill of the experimenter
errors consistent in magnitude and direction
systematic
human error
random error
errors that vary in magnitude and direction
random error
the SI units were a universally agreed system when
1960(adopted internationally )
1 inch to cm
2.54 cm
1 foot to meter
0.3048
1 foot to cm
30.48cm
1 ft to inches
12 inches
1 mile to meter
1609m
1 litre
10^-3 m^3
fundamental units
base units
there are _______ fundamental units
seven
the fundamental units
mass
length
Time
Electric current
Thermodynamic Temperature
Luminous Intensity
Quantity of substance
mass
Kg
Length
m
Time
s
Electric Current
A
Thermodynamic termperature
K
Luminous intensity
Candela(C)
Quantity of substance
mol
kilogram
the mass of a particular platinum-iridum cylinder, kept at the international bureau of weights and measures, servres, france
metre
the distance travelled by light in 1/299792458 sec0nd
seconds
the time interval of 9,192,631,770 periods or cycles of the duration of the radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom
ampere
is a constant current that will produce a force equal to 2 X 10^-7 newton per metre of length when maintained in two straight parallel conductors of infinite length of negligible circular cross section and placed one metre apart in the vaccum
kelvin
the kelvin is defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water
mole(mol)
the amount of a substance of a system which contains as many as there are carbon atoms in 0.012Kg of carbon-12
m^2
area
m^3
volume
Kgm^-3
density {mass/volume}
speed/velocity
ms^-1
ms^-2
Acceleration
Kgms^-2
force {mass X acceleration}
in terms of unit, impulse is the same as
momentum {Kgms^-1}
momentum
{Kgms^-1}
impulse
{Kgms^-1}
power/radiant flux
joules per second{watts} {force x Velocity}
energy/work done
newton meter{force X distance}
pressure
NM^-2 {Force/Area}
unit of plane angle
radian
surface tension
N/m
unit of solid angle
steridian
peta
10^15
tera
10^12
giga
10^9
mega
10^6
kilo
10^3
deci
10^-1
10^-2
centi
10^-3
milli
10^-6
micro
10^-9
nano
10^-12
pico
order of magnitude
an approximate measure of the size of a number equal to the logarithm(base 10) rounded to a whole number
the smallest power of 10 required to represent a number
the fundamental dimensions are
length mass and time
spring constant(spring stiffness constant)
unit
newton per metre
torque
force X perpendicular distance
Angular Velocity (ω)
Angular velocity represents the rate of change of angular displacement and is measured in radians per second (rad/s). Radians are dimensionless, so angular velocity has the same dimension as frequency (1/time).
The dimensional formula for angular velocity is:
\text{[ω]} = \text{T}^{-1}
Where T is time.
Viscous Force (F)
Viscous force is measured in the same units as force, typically in newtons (N).
The dimensional formula for force is:
F= MLT-2
Where:
• M is mass, • L is length, and • T is time.
Viscous Force (F)
Viscous force is measured in the same units as force, typically in newtons (N).
The dimensional formula for force is:
F= MLT-2
Where:
• M is mass, • L is length, and • T is time.
Viscous Force (F)
Viscous force is measured in the same units as force, typically in newtons (N).
The dimensional formula for force is:
\text{[F]} = \text{MLT}^{-2}
Where:
• M is mass, • L is length, and • T is time.
Viscous Force (F)
Viscous force is measured in the same units as force, typically in newtons (N).
The dimensional formula for force is:
\text{[F]} = \text{MLT}^{-2}
Where:
• M is mass, • L is length, and • T is time.
Viscosity (η)
Viscosity (dynamic viscosity) is measured in pascal-seconds (Pa·s) or equivalently in units of N·s/m² or kg/(m·s).
The dimensional formula for viscosity is:
\text{[η]} = \text{ML}^{-1}\text{T}^{-1}
Where:
• M is mass, • L is length, and • T is time.
The vector product is anti–commutative:
The vector product is anti–commutative: a × b = −b × a. Relations among the unit vectors for vector products are:
i×j=k j×k=i k×i=j
scalar quantities
can be described completely by their magnitudes
examples of scalar quantities
mass
area
volume
density
time
temperature
work
energy
power
vector quantities
can be described by their magnitude and direction
examples of vector quantities
displacement
velocity
acceleration
force
weight
momentum
The vector product (or cross product) of vectors a and b is a vector c whose mag- nitude is given by
c = absinφ
where φ is the smallest angle between a and b. The direction of c is perpendicular to the plane containing a and b with its orientation given by the right–hand rule. One way of using the right–hand rule is to let the fingers of the right hand bend (in their natural direction!) from a to b; the direction of the thumb is the direction of c = a × b.
1 pound =
4.448221615260 newtons (exactly)
Work is not a vector quantity; it is a scalar quantity. Here’s why:
Why Work is a Scalar:
1. Dot Product: The dot product of two vectors (force and displacement) results in a scalar quantity. Since work is defined as a dot product, it is inherently scalar. 2. No Direction: Work represents a measure of energy transfer, and energy does not have direction—it’s only concerned with magnitude. Thus, work does not have components or direction associated with it, like vectors do. 3. Magnitude Only: When calculating work, we are only concerned with the amount of force applied and the distance moved in the direction of the force. There’s no need for directionality, so work is considered scalar.
Clarifying Confusion:
• Force and displacement are vector quantities, but work is the result of a dot product between these vectors, stripping the result of direction and leaving only magnitude. • You might encounter quantities like torque or momentum, which are vector quantities because they have direction, but work is specifically scalar because it measures the energy transferred, not how or in which direction.
Work is not a vector quantity; it is a scalar quantity. Here’s why:
Why Work is a Scalar:
1. Dot Product: The dot product of two vectors (force and displacement) results in a scalar quantity. Since work is defined as a dot product, it is inherently scalar. 2. No Direction: Work represents a measure of energy transfer, and energy does not have direction—it’s only concerned with magnitude. Thus, work does not have components or direction associated with it, like vectors do. 3. Magnitude Only: When calculating work, we are only concerned with the amount of force applied and the distance moved in the direction of the force. There’s no need for directionality, so work is considered scalar.
Clarifying Confusion:
• Force and displacement are vector quantities, but work is the result of a dot product between these vectors, stripping the result of direction and leaving only magnitude. • You might encounter quantities like torque or momentum, which are vector quantities because they have direction, but work is specifically scalar because it measures the energy transferred, not how or in which direction.
If
A has a magnitude of 6 m and
B has a magnitude of 8 m, what is the maximum possible magnitude of
A−B?
The magnitude of
X−Y can never be:
(a) Positive
(b) Greater than the sum of
∣X∣ and
∣Y∣
(c) Equal to zero
(d) Equal to
∣X∣
The magnitude of
M+N is always:
(a) Less than the sum of
∣M∣ and
∣N∣
(b) Greater than
∣M∣ or
∣N∣, but not both
(c) Between the sum and the difference of
∣M∣ and
∣N∣
(d) Equal to the difference of
∣M∣ and
∣N∣
If the vectors
𝑈 and
V are perpendicular, their difference has:
(a) A magnitude greater than both
∣U∣ and
∣lV∣
(b) The same magnitude as the sum
(c) A smaller magnitude than their sum
(d) No magnitude
If the vectors
P and
𝑄point in exactly opposite directions, the magnitude of their difference is:
(a) Equal to the sum of their magnitudes
(b) Equal to zero
(c) Larger than the sum of their magnitudes
(d) The same as the magnitude of l
P
. If
∣A∣=5m and
∣B∣=3m, what is the maximum possible value of
∣A−B∣?
(a) 5 m
(b) 8 m
(c) 2 m
(d) 1 m
The magnitude of
R−S is equal to the difference of their magnitudes if:
(a)
R and
𝑆 are parallel
(b)
R and
𝑆 are perpendicular
(c) One vector is zero
(d) The vectors point in opposite directions
The magnitude of
T−U can be zero if:
(a)
T and
U have the same direction and magnitude
(b)
𝑇 and
U have different magnitudes
(c)
T is larger than
𝑈
(d)
T and
U are perpendicular
If A = 0 for a vector in the xy-plane, does it follow that Ax = -Ay? What can you say about Ax and Ay?
Can you find a vector quantity that has a magnitude of zero but components that are not zero?
Can you find a vector quantity that has a magnitude of zero but components that are not zero?
Can you find a vector quantity that has a magnitude of zero but components that are not zero?
