Definitions (Component 1) Flashcards
Quantity
In S.I. a quantity is represented by a number * a unit,
e.g. m = 3.0 kg
Scalar
A scalar is a quantity that has magnitude only.
Vector
A vector is a quantity that has magnitude and direction.
Resolving a vector
into components in
particular directions
This means finding vectors (the so-called components)
in these directions, which add together vectorially to
make the original vector, and so, together, are
equivalent to this vector
Density of a
material, ρ
Density = Mass/ Volume Unit: kg m^-3
or g cm^-3
in which mass and volume apply to any sample of the
material.
Moment (or torque) of
a force
The moment (or torque) of a force about a point is defined as the force * the perpendicular distance from the point to the line of action of the force, i.e. moment = F * d Unit: Nm [N.B. the unit is not J]
The principle of
moments
For a system to be in equilibrium, Sum of anticlockwise
moments about a point = Sum of clockwise moments about
the same point.
Centre of gravity
The centre of gravity is the single point within a body at
which the entire weight of the body may be considered
to act.
Displacement
The displacement of a point B from a point A is the
shortest distance from A to B, together with the
direction. Unit: m
Mean Speed
Mean Speed = total distance travelled/ total time taken
Unit: ms^-1
Instantaneous speed
Instantaneous speed = rate of change of distance
Unit: ms ^-1
Mean acceleration
Mean acceleration + Change in velocity/ time taken
Unit: ms^-2
Instantaneous
acceleration
The instantaneous acceleration of a body is its rate of
change of velocity. Unit: ms ^-2
Terminal velocity
The terminal velocity is the constant, maximum velocity
of an object when the resistive forces on it are equal
and opposite to the ‘accelerating’ force (e.g. pull of
gravity).
Force, F
A force on a body is a push or a pull acting on the body
from some external body.
Unit: N
Newton’s 3rd law
If a body A exerts a force on a body B, then B exerts
an equal and opposite force on A.
Σ F = m a
The mass of a body * its acceleration is equal to the
vector sum of the forces acting on the body. This
vector sum is called the resultant force
Momentum
The momentum of an object is its mass multiplied by
its velocity. (p = mv). It is a vector.
UNIT: kg ms ^-1
or Ns
Newton’s 2nd law
The rate of change of momentum of an object is
proportional to the resultant force acting on it, and
takes place in the direction of that force
The principle of
conservation of
momentum
The vector sum of the momenta of bodies in a system
stays constant even if forces act between the bodies,
provided there is no external resultant force.
Elastic collision
A collision in which there is no change in total kinetic
energy.
Inelastic collision
A collision in which kinetic energy is lost
Work, W
Work done by a force is the product of the magnitude
of the force and the distance moved in the direction of
the force.( W.D. = Fxcos θ )
Unit: J
Principle of
conservation of
energy
Energy cannot be created or destroyed, only
transferred from one form to another. Energy is a
scalar
Potential energy, Ep
This is energy possessed by an object by virtue of its
position. Ep = mgh Unit: J
Kinetic energy, Ek
This is energy possessed by an object by virtue of its
motion. Ek = ½mv2 Unit: J
Elastic potential
energy
This is the energy possessed by an object when it has
been deformed due to forces acting on it.
Eelastic = ½ Fx or ½ kx2
Unit: J
Energy
The energy of a body or system is the amount of work
it can do. Unit: J
Power, P
This is the work done per second, or energy
transferred per second.
Unit: W [= Js-1]
Period, T for a point
describing a circle
Time taken for one complete circuit.
Frequency, f
The number of circuits or cycles per second.
OR
The number of oscillations per second. UNIT: Hz
Radian
A unit of measurement of angles equal to about 57.3°,
equivalent to the angle subtended at the centre of a
circle by an arc equal in length to the radius. UNIT: rad
Angular
velocity, ω
For an object describing a circle at uniform speed, the
angular velocity ω is equal to the angle θ swept out by
the radius in time divided by t(ω = θ/t)
UNIT: rad s-1
Simple harmonic
motion (shm)
Shm occurs when an object moves such that its
acceleration is always directed toward a fixed point
and is proportional to its distance from the fixed point.
(a = – ω^2 x)
Alternative definition:
The motion of a point whose displacement x changes
with time t according to x = A sin (ω t + ε), where A, ω
and ε are constants. [Variations of this kind are said to
be sinusoidal.]
Period, T for an
oscillating body
The time taken for one complete cycle.
Amplitude, A of an
oscillating object
The maximum value of the object’s displacement (from
its equilibrium position).
Phase
The phase of an oscillation is the angle (ωt + ε) in the
equation x = A sin (ω t + ε). [ε is called the phase
constant.]
UNIT: rad
Free oscillations
[Natural oscillations]
Free oscillations occur when an oscillatory system
(such as a mass on a spring, or a pendulum) is
displaced and released.
[The frequency of the free oscillations is called the
system’s natural frequency.]
Damping
Damping is the dying away, due to resistive forces, of
the amplitude of free oscillations.
Critical damping
Critical damping is the case when the resistive forces
on the system are just large enough to prevent
oscillations occurring at all when the system is
displaced and released.
Forced oscillations
These occur when a sinusoidally varying ‘driving’ force
is applied to an oscillatory system, causing it to
oscillate with the frequency of the applied force.
Resonance
If, in forced vibrations, the frequency of the applied
force is equal to the natural frequency of the system
(e.g. mass on spring), the amplitude of the resulting
oscillations is large. This is resonance.
Ideal gas
An ideal gas strictly obeys the equation of state
pV = nRT, in which n is the number of moles, T is the
kelvin temperature and R is the molar gas constant.
R = 8.31 J mol-1 K
-1
. With the exception of very high
densities a real gas approximates well to an ideal gas.
The mole
The mole is the S.I. unit of an ‘amount of substance’. It
is the amount containing as many particles (e.g.
molecules) as there are atoms in 12 g of carbon-12.
Avogadro constant,
NA
This is the number of particles per mole.
NA = 6.02 X 10^23 mol^-1
Internal energy, U, of
a system
This is the sum of the kinetic and potential energies of
the particles of a system.
Heat, Q
This is energy flow from a region at higher temperature
to a region at lower temperature, due to the
temperature difference. In thermodynamics we deal
with heat going into or out of a system. It makes no
sense to speak of heat in a system
Work, W
If the system is a gas, in a cylinder fitted with a piston,
the gas does work of amount p* change in V when it exerts a
pressure p and pushes the piston out a small way, so
the gas volume increases by change in V. Work, like heat, is
energy in transit from (or to) the system.
First law of thermodynamics
The increase, U, in internal energy of a system is U = Q – W in which Q is the heat entering the system
and W is the work done by the system. Any of the
terms in the equation can be positive or negative, e.g.
if 100 J of heat is lost from a system Q = –100 J.
Specific heat
capacity, c
The heat required, per kilogram, per degree celsius or
kelvin, to raise the temperature of a substance.
UNIT: J kg^-1 K^-1
or J kg^-1 °C^-1
