Dynamics

Contents delivered by Dr Ya Huang (Unit Coordinator):

Ya.Huang@port.ac.uk

1.

Office: A0.12b

Force and motion

Displacement, velocity, acceleration equations; force; equilibrium; vector and scalar; moment; free-body diagram; friction; projectiles.

2.

Work and energy

Principle of work and energy; mechanical energy (kinetic and potential energy); conservation of mechanical energy; power; efficiency.

3.

Momentum and impulse

Conservation of momentum; elastic, inelastic collision; impulse.

4.

Motion in a circle

Angular and tangential motion; rotational kinetic energy; torque

(moment); transmission of power; centripetal, centrifugal acceleration;

*angular momentum.

5.

Simple Harmonic Motion

Pendulum system; simple spring-mass system; *damping, resonance.

For full contents of this unit: lecture notes, tutorial, tutorial solutions etc., log in to

Moodle: moodle.port.ac.uk

Reference

Lee, Stephen (2008). An Introduction to Mathematics for Engineers - Mechanics,

Hodder Education, London.

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Dynamics

The International System of Units – SI units

The base units (7 in total) we will be mainly dealing with in Dynamics are: mass…………. kilogram… kg

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. length………….metre………m The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. time……………second……..s The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

We will deal with in other topics: temperature .…Kelvin……….K

The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. amount of substance…mole…mol

The mole is the amount of substance of a system, which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol".

The other two are the ampere [A] and candela [cd]

All other units are derived quantities and are based on these units. Some examples are given below.

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Derived units:

Force:

The unit of force is the ‘newton’ (N) defined from Newton’s second law: force = mass x acceleration, or

F=mxa

then 1 newton (N) is the force that will accelerate 1 kg at 1 m/s2

⎡ kgm ⎤

So 1 [N] = 1 ⎢

⎥ note that the terms in square brackets define the unit N in terms

⎣ s2 ⎦ of the fundamental units mass, length, time.

Energy

or work done by a force:

Energy can be quantified by work done by a force:

Work or energy = force x distance, or

W=Fxs

The derived unit for energy is the ‘joule’ (J):

⎡ kgm2 ⎤

⎡ kgm ⎤

1 [J] = 1 [Nm] = 1 ⎢ 2 m⎥ = 1⎢ 2 ⎥

⎣ s

⎦

⎢ s ⎥.

⎣

⎦

Power

or energy rate:

Power can be quantified by the rate of energy transfer i.e. joules per second: power = energy / time = work done / time

P=W/t=Fxs/t

The derived unit for power is the ‘watt’ (W):

⎡ kgm2 ⎤

⎡⎛ kgm ⎞⎛ m ⎞ ⎤

J

Nm

1[W] = 1[ ] = 1[

] = 1⎢⎜ 2 ⎟ ⎜ ⎟⎥ = 1⎢ 3 ⎥ s s

⎢ s ⎥

⎣⎝ s ⎠ ⎝ s ⎠ ⎦

⎣

⎦

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.

Examples of the derived units

Derived quantity

Name

Symbol In other SI units

In SI base units

plane angle

radian

rad

m/m

frequency

hertz

Hz

s–1

force

newton

N

m kg s–2

pressure, stress

pascal

Pa

N/m2

m–1 kg s–2

energy, work, amount joule of heat

J

Nm

m2 kg s–2

power, radiant flux

watt

W

J/s

m2 kg s–3

electric charge, amount of electricity

coulomb

C

electric potential difference, electromotive force

volt

V

W/A

m2 kg s–3 A–1

capacitance

farad

F

C/V

m–2 kg–1 s4 A2

electric resistance

ohm

Ω

V/A

m2 kg s–3 A–2

electric conductance siemens