**Chapter 1 Introduction: Measurement, Physical Quantities and Units **

Galaxies are immense as atoms are small. Yet, the same laws of physics govern both, and all the rest of nature, an indication of the underlying unity in the universe. The laws of physics are surprisingly few in number, implying an underlying simplicity to nature’s apparent complexity.

**Physics: An introduction **

The physical universe is enormously complex in its detail. Quarks, lightning, gravity, flowers, etc.

We have found that nature is remarkably cooperative – it exhibits the underlying order and simplicity that we so value.

The unifying aspect of physical laws and the basic simplicity of nature form the underlying themes of this text.

**Science and the Realm of Physics **

Science consists of the laws that are the general truths of nature and the body of knowledge they encompass.

Physics is the most basic of the sciences, concerning itself with the interactions of energy, matter, space, and time, and especially with questions of what underlies every phenomenon.

We discover physics by learning how to measure the quantities involved in physics. Among these quantities are length, time, mass, temperature, pressure and electrical current.

**Applications of Physics **

You need not be a scientist to use physics. On the contrary, a knowledge of physics is useful in everyday
situations as well as in nonscientific professions. It can help you understand how microwave oven works,
**etc.. **

Physics is the foundation of many important disciplines and contributes directly to other. Chemistry, for example – since it deals with the interactions of atoms and molecules – is rooted in atomic and molecular physics.

The disciplines of biology, chemistry, and physics are needed to understand membranes. [Human and Medical application]

**Models, Theories, and Laws; The Role of Experimentation **

**A model is a mental image or analogy to objects or phenomena that we can experience directly. **

**A theory is usually a larger-scale and more broadly applicable generalization than a model and often **
seeks to describe nature with mathematical precision. Some theories include models to help visualize
phenomena, whereas others do not.

**The designation law is reserved for a concise and very general statement, such as the law that energy is **
conserved in any process, or Newton’s second law of motion.

**Less broadly applicable statements are usually called principles (such as Pascal’s principle, which is **
applicable only in fluids, but the distinction between laws and principles often is not carefully made.

The models, theories, and laws that we devise sometimes imply the existence of objects or phenomena as yet unobserved. A theory or a law needs to be verified by an experiment. A law may be completely overthrown, or may be modified, as a result of an experiment.

**The evolution of natural philosophy into modern physics **

Physics was not always a separate and distinct discipline and is not now isolated from other sciences.

The word physics comes from Greek, meaning nature. They study of nature came to be called “naturally
philosophy”. From ancient times through the Renaissance, natural philosophy encompassed many fields,
including astronomy, biology, chemistry, physics, mathematics and medicine. Physics as it developed
from the Renaissance to the end of the 19^{th}** century is called classical physics. **

**Modern physics itself consists of two revolutionary theories, relativity and quantum mechanics. **

**Quantum mechanics must be used for objects smaller than can be seen with a microscope. **

**Physical Quantities and Units **

**We define a physical quantity either by specifying how it is measured or by stating how it is calculated **
from other measurements.

**We measure each physical quantity in its own units, by comparison with a standard. The unit is a unique **
name we assign to measures of that quantity – for example, meter (m) for the quantity length. The
**standard corresponds to exactly 1.0 unit of the quantity. **

**SI Units: Fundamental and derived units **

Many SI derived units are defined in terms of these base units. For example, the SI unit for power, called the watt (W), is defined in terms of the base units of mass, length and time.

**Units of Time, Length and Mass: The Second, Meter and Kilogram **
**Length **

**Time **

**Mass **

**Metric Prefixes **

**Measurements, accuracy, and uncertainty; significant figures **

**The uncertainty in a measurement is an estimate of the amount it can be off from the “true” value. **

**Using the method of significant figures, the rule is that the last digit written down is the first digit with **
some uncertainty. Special consideration is given to zeros when counting significant figures.

**Significant figures in calculations **

The result has the same number of significant figures as the quantity having the least significant figures entering into the calculation.

**Problems: **

**1.2, 1.37**

**Chapter 2 Kinematics **

Kinematics is defined to be the study of motion without regard to mass or force.

**2.1 Displacement **

**We define displacement to be the change in position of an object **

In 1D: ∆*x*=*x*_{2}−*x*_{1}

Distance is defined to be the magnitude of size of displacement. Distance has no direction and, hence has no sign.

**Vectors and Scalars **

**Any quantity with both magnitude and direction is defined to be a vector. For example, displacement is **
a vector.

**Any quantity with a magnitude only, but no direction, is defined to be a scalar. For example, **
*temperature and pressure are both scalars. *

**2.2 Time, Velocity and Speed **

**In physics the definition of time is simple – time is change. It is impossible to know that time has passed **
unless something changes.

* We define elapsed time t*∆ , to be the difference between the ending time and beginning time:

1

2 *t*

*t*
*t*= −

∆

**Average velocity **

_

*v* is precisely defined to be displacement (change in position) divided by the time of
**travel and to have the same direction as displacement. **

1 2

1 2 _

*t*
*t*

*x*
*x*
*t*
*v* *x*

−

= −

∆

= ∆

* Instantaneous velocity v* is the average velocity at a specific instant in time, i.e., ∆t→0

**Instantaneous speed is simply defined to be the magnitude of instantaneous velocity. **

**2.3 Acceleration **

**Acceleration **

_

*a* **is the rate at which the velocity changes. In symbols, average acceleration is defined **
to be

1 2

1 2 _

*t*
*t*

*v*
*v*
*t*
*a* *v*

−

= −

∆

= ∆

*Acceleration is a vector in the same direction as the change in velocity. *

**Instantaneous acceleration, in symbol, is defined as **

*dt*
*dv*
*t*
*t*

*v*
*v*
*t*

*a* *v*

*t*

*t* =

−

= −

∆

= ∆

→

∆

→

∆ 2 1

1 2 0

0 lim

lim

**2.4 Motion equations for constant acceleration in one dimension **

**2.6 Falling objects **

**An object falling without air resistance or friction is defined to be in Free-fall. **

**Taken from Fig. 2. 10 **

m/s2

8 .

=9
*g*

**Taken from Fig. 2.13 **

**Problems: 2.16, 2.31 **

**Chapter 3 Two-dimensional Kinematics **

The graphical addition of vectors:

Adding vectors graphically (head to tail)

**Taken from Fig. 3.5 **

**Vector can be added in any order. A + B = B + A **

**Subtracting vector graphically **

**A – B = A + (-B) **

**Analytical methods of vector addition **

**Taken from Fig. 3.19 (Halliday) **

**Unit vector **

**Right-hand rule **

**Projectile Motion **

**Taken from Figure 3.12 **

**Horizontal **

**Vertical **

**The Equation of the path **

**Horizontal range **

**Relative velocity and classical relativity **

**Taken from Halliday **

**Inertial reference frames (constant velocity) **

**Problems: 3.42, 3.47 **

**Chapter 4 Dynamics **

Newton’s laws of Motion

**4.1 Force **

**Restoring force **

**Taken from Figure 4.2 **

**Hooke’s law: ** *F*r *kx*r

−

=
**Newton’s first law of motion **

A body at rest remains at rest, or if in motion remains in motion at constant velocity, unless acted on by a net external force.

**Mass **

The property by which a body remains at rest or remain in motion with constant velocity is called inertia,
**and Newton’s first law is often called the law of inertia. **

*F*
*a*∝net

*m*
*a* net *F*

=

**Newton’s second law of motion**

*ma*
*F* =
net

**Newton’s third law of motion **

Whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the one it exerts.

**Weight and the force of gravity **

*mg*
*w*=

**Taken from Figure 4.8 **

**Weight on an incline, a two-dimensional problem **

**Friction **

The magnitude of static friction
*N*

*f** _{s}* ≤

*µ*

*, where*

_{s}*µ is the coefficient of static friction*

_{s}The magnitude of kinetic friction

*N*

*f** _{k}* =

*µ*

*, where*

_{k}*µ is the coefficient of kinetic friction*

_{k}**Taken from Fig. 4.A **

Figure 4.21 shows a 75.0 kg man standing on a bathroom scale in an elevator. Calculate the scale
reading: (a) if the elevator accelerates upward at a rate of 1.20 m/s^{2}, and (b) if the elevator moves
upward at a constant speed.

**Taken from Figure 4.21 **

**Sol: **

**a) ** net *F* =*ma*
*ma*
*w*
*F** _{s}* − =

*ma*
*mg*
*F** _{s}* = +

N 825 ) m/s 80 . 9 )(

kg 0 . 75 ( ) m/s 20 . 1 )(

kg 0 . 75

( ^{2} + ^{2} =

*s* =
*F*

b) *F**s* =(75.0 kg)(9.80 m/s^{2})=735 N

c) Free-fall?

**Problems: 4.3, 4.30 **

**Chapter 5 Statics, torque, and elasticity **

**5.1 The first condition for equilibrium **

0
net *F* =

**5.2 The second condition for equilibrium **

0
net *τ* =

Def. *r*r *F*r

×

=
*τ*

**Taken from Halliday **
**Center of Mass; center of gravity **

...

...

3 2 1

3 3 2 2 1 1

CM + + +

+ +

= +

*m*
*m*
*m*

*r*
*m*
*r*
*m*
*r*
*r* *m*

...

...

3 3 2 2 1 1

3 3 3 2 2 2 1 1 1

CG + + +

+ +

= +

*g*
*m*
*g*
*m*
*g*
*m*

*r*
*g*
*m*
*r*
*g*
*m*
*r*
*g*
*r* *m*

If g is uniform, then *r** _{CM}* =

*r*

*.*

_{CG}**Stability **

**A system is said to be in stable equilibrium if, when displaced from equilibrium, it experiences a net **
force or torque in a direction opposite to the direction of the displacement.

**A system is in unstable equilibrium if, when displaced from equilibrium, it experiences a net force or **
torque in the same direction as the displacement from equilibrium.

**A system is in neutral equilibrium if its equilibrium is independent of displacement from its original **
position.

**Forces and torques in muscles and joints **

Taken from Figure 5.19

Figure 5.19 shows a forearm holding a book and a schematic diagram of am analogous lever system.

The triceps is assumed to be relaxed.

Ex. Calculate the force the biceps muscle must exert to hold the forearm and its load as shown in Fig.

5.19, and compare this force with the weight of the forearm plus its load.

Sol: net*τ* =0
Pivot: the joint

*B*
*b*

*a* *rw* *rF*

*w* _{3} _{1}

r2 + =

*B*
*b*

*a* *F*

*r*
*w*
*r*

*w* + =

1 3

r2

N

=470
*F**B*

38
.
7 7
.
63
F_{B} 470

=
+ * _{b}* =

*a* *w*

*w* !

Muscles exert bigger forces than you might think. Very large forces are also created in the joint. Because the way things are put together, joints and muscles often exert forces in opposite direction. Forces in muscles are largest when their load is a long distance from the joint. Racket sports, such as tennis, exaggerate this effect by extending the arm. Tennis elbow… .

Ex. Do not lift with your back

Consider the person lifting a heavy box with his back, shown in Fig. 5.22. (a) Calculate the force in the
back muscle *F** _{B}* needed to support the upper body plus the box and compare this with their weight. The
mass of the upper body is 55.0 kg and that of the box is 30.0 kg (b) Calculate the magnitude and
direction of the force

*F exerted by the vertebrae on the spine at the indicated pivot point.*

_{v}Sol:

(a) net*τ* =0 Using the perpendicular lever arms given in the figure.

) )(

cm 00 . 8 ( ) m/s 80 . 9 )(

kg cm)(30.0 0

. 50 ( ) m/s 80 . 9 )(

kg cm)(55.0

(35.0 ^{2} + ^{2} = *F*_{B}

N 10 20 .

4 × ^{3}

*B* =
*F*

04 . 833 5

10 20 . 4

F_{B} ^{3}

× =
+ * _{box}* =

*ub* *w*

*w*

**Taken from Figure 5.22 **

(b) More important in terms of its damage potential is the force on the vertebrae*F . ** _{V}*
0

net
net *F** _{y}* =

*F*

*=*

_{x}0 0 . 29

sin =

−

−

− _{ub}_{box}_{B}^{°}

*Vy* *w* *w* *F*

*F*

N 10 87 .

2 × ^{3}

*Vy* =
*F*

Similarly *F** _{Vx}* −

*F*

*cos29.0*

_{B}^{°}=0

N 10 67 .

3 × ^{3}

*Vy* =
*F*

N 10 66 .

4 ^{3}

2

2+ = ×

= _{Vx}_{Vy}

*V* *F* *F*

*F*

°

− =

=tan ^{1}( ) 38.0

*Vx*
*Vy*

*F*
*θ* *F*

60 . 833 5

10 66 .

F_{V} 4 ^{3}

× =
+ * _{box}* =

*ub* *w*

*w*

This force is 5.60 times greater than it would be if the person were standing erect. The trouble with the back is not so much that the forces are large – because similar forces are created in our hips, knees and ankles – but that our spines are relatively weak.

**Elastic **

**Taken from Halliday **

**Stress = γ x Strain **

**Problems: 5.19, 5.35 **

**Chapter 6 Work, energy and power **

**Work and kinetic energy **

**Taken from Halliday **

**Taken from Halliday **

**Conservative forces and potential energy **

**A conservative force is one, like gravity, for which work done by or against it depends only on the **
starting and ending points of a motion and not on the path taken.

Spring force *F*r *kx*r

−

=

**Nonconservative forces: open systems **

**A crate plus a friction floor **

**Power **

**Conservation of energy **

**Kinetic energy **

**Potential energy **

**Mechanical energy **

**Problems: 6.15, 6.33 **

**Chapter 7 Linear Momentum **

Linear momentum and force
**v**

**p**=m

**v**
**v**

**p**=∆ = ∆

∆ (m ) *m* if m is constant

**v** **a**

**F** **p** *m*

*t*
*m*

*t* =

∆

= ∆

∆

= ∆ net

Elastic collision: the total kinetic energy is conserved.

the total linear momentum is conserved as well.

Inelastic collision: the total kinetic energy is not conserved.

the total linear momentum is conserved.

Elastic collision: Stationary target

Special cases:

Moving targets

Elastic collisions in 2D

**Taken from Halliday **

**Rocket **

**A system with variable mass **

**Rocket scientist? **

**Taken from Halliday **

Conservation of the linear momentum

**Problems: 7.11, 7.35 **

**Chapter 26 Special Relativity **

Albert Einstein

**Inertial reference frames: constant velocity **

Space and time are actually entangled: the time between two events depends on how far apart they occur, and vice versa.

The Ultimate speed

**Taken from Halliday **

**Testing the speed of light postulate **

Neutral pion

Measuring an event

An event is something that happens, to which an observer can assign three space coordinates and one time coordinate.

The speed of light!! We need to construct an imaginary array of measuring rods and clocks thoroughout the observer’s frame.

**Taken from Halliday **

**The relativity of simultaneity **

If two observers are in relative motion, they will not, in general, agree as to whether two events are simultaneous. If one observer finds them to be simultaneous, the other generally will not, and conversely.

**The relativity of time **

An interesting experiment

Sally on the train with constant velocity. She has a light source, a mirror, and a clock.

Sam in the station

They want to measure the time interval between two events: event 1 and event 2.

**Taken from Halliday **

**When two events occur at the same location in an inertial reference frame, the time interval between **
**them, measured in that frame, is called the proper time interval. Measurements of the same time **
interval from any other inertial reference frame are always greater.

**Time dilation!! **

**Tests: **

**Microscopic clocks **

**Macroscopic clicks **

**Macroscopic clocks **

**Example: Your starship passes Earth with a relative speed of 0.9990c. After traveling 10.0 year (your **
time), you stop at lookout post LP13, turn, and then travel back to Earth with the same relative speed.

The trip back takes another 10.0 year (your time). How long does the round trip take according to measurements made on Earth?

**Sol: **

**Your time is the proper time. **

**Back to the future!! **

**Taken from Urone **
**The Relativity of length **

**Galilean and Lorentz transformations **

∞

→

*c* then *γ* →1

Galilean transformation is equivalent to Lorentz transformation.

**Consequences of the Lorentz transformation **

**The relativity of velocities **

**Taken from Halliday **

**Lorentz transformation **

**Doppler effect for light **

**Transverse Doppler effect **

**Taken from Halliday **

**Relativistic momentum **

**Relativistic energy **

**Relativistic kinetic energy **

2

2 *mc*

*mc*
*K*+ =*γ*

4 2 2 2 2)

(*K* +*mc* =*γ* *m* *c*

4 2 2 4 2 2

2 2*Kmc* *m* *c* *m* *c*

*K* + + =*γ*

) )(

( ) )(

( )

1 (

2 _{2} _{2} ^{2} ^{4}

2 4

2 2 2

2 2

2 2

2 4

2 2 2

2 *m* *c*

*v*
*c*
*c* *v*
*v* *m*
*c*

*v*
*c*
*v*
*c*
*c* *c*
*m*
*Kmc*

*K* = −

−

− −

= −

−

=

+ *γ*

*mv*
*p*=*γ*

2 2

2 2 2

2 2 2

2 2 2 2 2 2

*v*
*c*

*v*
*c*
*m*

*c*
*v*
*c*

*v*
*v* *m*

*m*

*p* = −

= −

=*γ*

2 2

2 4 2 2 2

*v*
*c*

*v*
*c*
*c* *m*

*p* = −

2 2 2

2 2*Kmc* *p* *c*

*K* + =

*K*
*mc*
*E*= ^{2} +

2 2 2 2

2 4

2

2 *m* *c* 2*mc* *K* *K* (*pc*) (*mc* )

*E* = + + = +

**Taken from Halliday **

**Problems: 26.4, 26.19, 26.23 **