Zuhairusnizam Md Darus Website:

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Zuhairusnizam Md Darus Website: http://zuhairusnizam.uitm.eu.my
PHYSICS I PHY 093 Zuhairusnizam Md Darus Phone Office : Mobile: Website: UiTM Shah Alam : Unit Percetakan Universiti (UPENA) UiTM Puncak Alam :Aras 4

093 B R E A K (18/7 – 25/7) RECOMMENDED TEXT:
PHYSICS For Scientists & Engineers With Modern Physics by Giancoli, 4th Edition REFERENCES: Fundamental of Physics by Halliday, Resnick, Walker;6th or 7th Ed., John Wiley &Sons, Inc. Physical Quantities and Units Base Quantities and SI Units Significant Figures Conversion of Units Dimensional Analysis Scalars and Vectors Laws of Thermodyn Heat Capacity of Gases Work and Internal Energy First Law of Thermodynamics Second Law of Thermodynamics 1, 2 15 Ch 1, 3, 7 Ch 19, 20 ASSESSMENT: TESTS – 30% LAB REPORTS – 10% FINAL EXAM – 60 % Mechanics of Motion Motion with Constant Acceleration (1 – D) 3 Ch 2 Gases and Kinetic Theory Gas Laws and Absolute Temp Kinetic Theory of Gases 14 Mechanics of Motion Motion with Constant Acceleration (2 – D) 4 Ch 18 Ch 3 Newton’s Laws and Applications Circular Motion Uniform Circular Motion Centripetal and Angular Accn Centripetal Force Temperature and Heat Temp and Thermal Eqm Thermometers and Temp Scale Thermal Expansion of Solids n Liquids Heat 13 093 5 Ch 17 Ch 4, 5 12 States of Matter Solid – Stress & Strain Young’s Modulus Fluids – Density and Pressure Archimedes’ Principle Bernoulli’s Principle 6 Ch 12, 13 Ch 7, 8 Work and Energy Work by a Varying Force KE n W-KE Theorem PE Conservation of Energy 11 Gravitation Newton’s Law of Gravitation Gravitational Field Strength Gravitational Potential Realtionship bet g and G Satellite Motion in Cicular Orbits Escape velocity 7 Ch 6 9 Ch 9 Ch 10, 11 Rotational Motion Rotational Dynamics Angular Momentum Momentum, Impulse and Collissions 10 8 Ch 12 B R E A K (18/7 – 25/7) Zuhairusnizam Md Darus Phoe: Off : Unit Penerbitan Universiti (UPENA) Statics Equilibrium of Particles Free-body diagram Equilibrium of Rigid Bodies Prepared by Prof Madya Ahmad Abd Hamid, May 2010

LECTURES

Units of Chapter 1 The Nature of Science Models, Theories, and Laws
Measurement and Uncertainty; Significant Figures Units, Standards, and the SI System Converting Units Order of Magnitude: Rapid Estimating Dimensions and Dimensional Analysis Copyright © 2009 Pearson Education, Inc.

1-1 The Nature of Science Observation: important first step toward scientific theory; requires imagination to tell what is important Theories: created to explain observations; will make predictions Observations will tell if the prediction is accurate, and the cycle goes on. No theory can be absolutely verified, although a theory can be proven false. Copyright © 2009 Pearson Education, Inc.

1-1 The Nature of Science How does a new theory get accepted?
Predictions agree better with data Explains a greater range of phenomena Example: Aristotle believed that objects would return to a state of rest once put in motion. Galileo realized that an object put in motion would stay in motion until some force stopped it. Copyright © 2009 Pearson Education, Inc.

1-1 The Nature of Science The principles of physics are used in many practical applications, including construction. Communication between architects and engineers is essential if disaster is to be avoided. Figure 1-1. Caption: (a) This Roman aqueduct was built 2000 years ago and still stands. (b) The Hartford Civic Center collapsed in 1978, just two years after it was built. Copyright © 2009 Pearson Education, Inc.

1-2 Models, Theories, and Laws
Models are very useful during the process of understanding phenomena. A model creates mental pictures; care must be taken to understand the limits of the model and not take it too seriously. A theory is detailed and can give testable predictions. A law is a brief description of how nature behaves in a broad set of circumstances. A principle is similar to a law, but applies to a narrower range of phenomena. Copyright © 2009 Pearson Education, Inc.

1-3 Measurement and Uncertainty; Significant Figures
No measurement is exact; there is always some uncertainty due to limited instrument accuracy and difficulty reading results. The photograph to the left illustrates this – it would be difficult to measure the width of this board more accurately than ± 1 mm. Figure 1-2. Caption: Measuring the width of a board with a centimeter ruler. The uncertainty is about ±1 mm. Copyright © 2009 Pearson Education, Inc.

Estimated uncertainty is written with a ± sign; for example: 8.8 ± 0.1 cm. Percent uncertainty is the ratio of the uncertainty to the measured value, multiplied by 100: Copyright © 2009 Pearson Education, Inc.

The number of significant figures is the number of reliably known digits in a number. It is usually possible to tell the number of significant figures by the way the number is written: 23.21 cm has four significant figures. 0.062 cm has two significant figures (the initial zeroes don’t count). 80 km is ambiguous—it could have one or two significant figures. If it has three, it should be written 80.0 km. Copyright © 2009 Pearson Education, Inc.

When multiplying or dividing numbers, the result has as many significant figures as the number used in the calculation with the fewest significant figures. Example: 11.3 cm x 6.8 cm = 77 cm. When adding or subtracting, the answer is no more accurate than the least accurate number used. The number of significant figures may be off by one; use the percentage uncertainty as a check. Copyright © 2009 Pearson Education, Inc.

Calculators will not give you the right number of significant figures; they usually give too many but sometimes give too few (especially if there are trailing zeroes after a decimal point). The top calculator shows the result of 2.0/3.0. The bottom calculator shows the result of 2.5 x 3.2. Figure 1-3. Caption: These two calculators show the wrong number of significant figures. In (a), 2.0 was divided by 3.0. The correct final result would be In (b), 2.5 was multiplied by 3.2.The correct result is 8.0. Copyright © 2009 Pearson Education, Inc.

Conceptual Example 1-1: Significant figures. Using a protractor, you measure an angle to be 30°. (a) How many significant figures should you quote in this measurement? (b) Use a calculator to find the cosine of the angle you measured. Figure 1-4. Caption: Example 1–1. A protractor used to measure an angle. Response: (a) If you look at a protractor, you will see that the precision with which you can measure an angle is about one degree (certainly not 0.1°). So you can quote two significant figures, namely, 30° (not 30.0°). (b) If you enter cos 30° in your calculator, you will get a number like However, the angle you entered is known only to two significant figures, so its cosine is correctly given by 0.87; you must round your answer to two significant figures. Copyright © 2009 Pearson Education, Inc.

Scientific notation is commonly used in physics; it allows the number of significant figures to be clearly shown. For example, we cannot tell how many significant figures the number 36,900 has. However, if we write 3.69 x 104, we know it has three; if we write x 104, it has four. Much of physics involves approximations; these can affect the precision of a measurement also. Copyright © 2009 Pearson Education, Inc.

Accuracy vs. Precision Accuracy is how close a measurement comes to the true value. Precision is the repeatability of the measurement using the same instrument. It is possible to be accurate without being precise and to be precise without being accurate! Copyright © 2009 Pearson Education, Inc.

1-4 Units, Standards, and the SI System
Quantity Unit Standard Length Meter Length of the path traveled by light in 1/299,792,458 second Time Second Time required for 9,192,631,770 periods of radiation emitted by cesium atoms Mass Kilogram Platinum cylinder in International Bureau of Weights and Measures, Paris Copyright © 2009 Pearson Education, Inc.

We will be working in the SI system, in which the basic units are kilograms, meters, and seconds. Quantities not in the table are derived quantities, expressed in terms of the base units. Other systems: cgs; units are centimeters, grams, and seconds. British engineering system has force instead of mass as one of its basic quantities, which are feet, pounds, and seconds. Copyright © 2009 Pearson Education, Inc.

1-5 Converting Units Unit conversions always involve a conversion factor. Example: 1 in. = 2.54 cm. Written another way: 1 = 2.54 cm/in. So if we have measured a length of 21.5 inches, and wish to convert it to centimeters, we use the conversion factor: Copyright © 2009 Pearson Education, Inc.

1-5 Converting Units Example 1-2: The 8000-m peaks.
The fourteen tallest peaks in the world are referred to as “eight-thousanders,” meaning their summits are over 8000 m above sea level. What is the elevation, in feet, of an elevation of 8000 m? Figure 1-6. Caption: The world’s second highest peak, K2, whose summit is considered the most difficult of the “8000-ers.” K2 is seen here from the north (China). Answer: An elevation of 8000 m is 26,247 ft above sea level. Copyright © 2009 Pearson Education, Inc.

1-6 Order of Magnitude: Rapid Estimating
A quick way to estimate a calculated quantity is to round off all numbers to one significant figure and then calculate. Your result should at least be the right order of magnitude; this can be expressed by rounding it off to the nearest power of 10. Diagrams are also very useful in making estimations. Copyright © 2009 Pearson Education, Inc.

Example 1-5: Volume of a lake. Estimate how much water there is in a particular lake, which is roughly circular, about 1 km across, and you guess it has an average depth of about 10 m. Figure 1-7. Caption: Example 1–5. (a) How much water is in this lake? (Photo is of one of the Rae Lakes in the Sierra Nevada of California.) (b) Model of the lake as a cylinder. [We could go one step further and estimate the mass or weight of this lake. We will see later that water has a density 1000 kg/m3, of so this lake has a mass of about (103 kg/m3)(107 m3) ≈ 1010 kg, which is about 10 billion kg or 10 million metric tons. (A metric ton is 1000 kg, about 2200 lbs, slightly larger than a British ton, 2000 lbs.)] Answer: The volume of the lake is about 107 m3. Copyright © 2009 Pearson Education, Inc.

Example 1-6: Thickness of a page. Estimate the thickness of a page of your textbook. (Hint: you don’t need one of these!) Figure 1-8. Caption: Example 1–6. Micrometer used for measuring small thicknesses. Answer: Measure the thickness of 100 pages. You should find that the thickness of a single page is about 6 x 10-2 mm. Copyright © 2009 Pearson Education, Inc.

Example 1-7: Height by triangulation. Estimate the height of the building shown by “triangulation,” with the help of a bus-stop pole and a friend. (See how useful the diagram is!) Figure 1-9. Caption: Example 1–7. Diagrams are really useful! Answer: The building is about 15 m tall. Copyright © 2009 Pearson Education, Inc.

Example 1-8: Estimating the radius of Earth. If you have ever been on the shore of a large lake, you may have noticed that you cannot see the beaches, piers, or rocks at water level across the lake on the opposite shore. The lake seems to bulge out between you and the opposite shore—a good clue that the Earth is round. Suppose you climb a stepladder and discover that when your eyes are 10 ft (3.0 m) above the water, you can just see the rocks at water level on the opposite shore. From a map, you estimate the distance to the opposite shore as d ≈ 6.1 km. Use h = 3.0 m to estimate the radius R of the Earth. Figure Caption: Example 1–8, but not to scale. You can see small rocks at water level on the opposite shore of a lake 6.1 km wide if you stand on a stepladder. Answer: This calculation gives the radius of the Earth as 6200 km (precise measurements give 6380 km). Copyright © 2009 Pearson Education, Inc.

1-7 Dimensions and Dimensional Analysis
Dimensions of a quantity are the base units that make it up; they are generally written using square brackets. Example: Speed = distance/time Dimensions of speed: [L/T] Quantities that are being added or subtracted must have the same dimensions. In addition, a quantity calculated as the solution to a problem should have the correct dimensions. Copyright © 2009 Pearson Education, Inc.

1-7 Dimensions and Dimensional Analysis
Dimensional analysis is the checking of dimensions of all quantities in an equation to ensure that those which are added, subtracted, or equated have the same dimensions. Example: Is this the correct equation for velocity? Check the dimensions: Wrong! Copyright © 2009 Pearson Education, Inc.

Summary of Chapter 1 Theories are created to explain observations, and then tested based on their predictions. A model is like an analogy; it is not intended to be a true picture, but to provide a familiar way of envisioning a quantity. A theory is much more well developed, and can make testable predictions; a law is a theory that can be explained simply, and that is widely applicable. Dimensional analysis is useful for checking calculations. Copyright © 2009 Pearson Education, Inc.

Summary of Chapter 1 Measurements can never be exact; there is always some uncertainty. It is important to write them, as well as other quantities, with the correct number of significant figures. The most common system of units in the world is the SI system. When converting units, check dimensions to see that the conversion has been done properly. Order-of-magnitude estimates can be very helpful. Copyright © 2009 Pearson Education, Inc.

Chapter 3

Chapter 3 Vectors

3-1 Vectors and Scalars A vector has magnitude as well as direction.
Some vector quantities: displacement, velocity, force, momentum A scalar has only a magnitude. Some scalar quantities: mass, time, temperature

3-2 Addition of Vectors—Graphical Methods
For vectors in one dimension, simple addition and subtraction are all that is needed. You do need to be careful about the signs, as the figure indicates.

If the motion is in two dimensions, the situation is somewhat more complicated. Here, the actual travel paths are at right angles to one another; we can find the displacement by using the Pythagorean Theorem.

Adding the vectors in the opposite order gives the same result:

Even if the vectors are not at right angles, they can be added graphically by using the tail-to-tip method.

The parallelogram method may also be used; here again the vectors must be tail-to-tip.

3-3 Subtraction of Vectors, and Multiplication of a Vector by a Scalar
In order to subtract vectors, we define the negative of a vector, which has the same magnitude but points in the opposite direction. Then we add the negative vector.

3-3 Subtraction of Vectors, and Multiplication of a Vector by a Scalar
A vector can be multiplied by a scalar c; the result is a vector c that has the same direction but a magnitude cV. If c is negative, the resultant vector points in the opposite direction.

3-4 Adding Vectors by Components
Any vector can be expressed as the sum of two other vectors, which are called its components. Usually the other vectors are chosen so that they are perpendicular to each other.

If the components are perpendicular, they can be found using trigonometric functions.

The components are effectively one-dimensional, so they can be added arithmetically.

Draw a diagram; add the vectors graphically. Choose x and y axes. Resolve each vector into x and y components. Calculate each component using sines and cosines. Add the components in each direction. To find the length and direction of the vector, use: and .

Example 3-2: Mail carrier’s displacement. A rural mail carrier leaves the post office and drives 22.0 km in a northerly direction. She then drives in a direction 60.0° south of east for 47.0 km. What is her displacement from the post office?

Example 3-3: Three short trips. An airplane trip involves three legs, with two stopovers. The first leg is due east for 620 km; the second leg is southeast (45°) for 440 km; and the third leg is at 53° south of west, for 550 km, as shown. What is the plane’s total displacement?

3-5 Unit Vectors Unit vectors have magnitude 1.
Using unit vectors, any vector can be written in terms of its components:

3-6 Vector Kinematics In two or three dimensions, the displacement is a vector:

3-6 Vector Kinematics As Δt and Δr become smaller and smaller, the average velocity approaches the instantaneous velocity.

7-2 Scalar Product of Two Vectors
Definition of the scalar, or dot, product: Therefore, we can write: Figure 7-6. Caption: The scalar product, or dot product, of two vectors A and B is A·B = AB cos θ. The scalar product can be interpreted as the magnitude of one vector (B in this case) times the projection of the other vector, A cos θ, onto B.

7-2 Scalar Product of Two Vectors
Example 7-4: Using the dot product. The force shown has magnitude FP = 20 N and makes an angle of 30° to the ground. Calculate the work done by this force, using the dot product, when the wagon is dragged 100 m along the ground. Figure 7-7. Caption: Example 7-4. Work done by a force FP acting at an angle θ to the ground is W = FP·d. Answer: W = 1700 J.

11-2 Vector Cross Product; Torque as a Vector
The vector cross product is defined as: The direction of the cross product is defined by a right-hand rule: Figure The vector C = A x B is perpendicular to the plane containing A and B; its direction is given by the right-hand rule.

The cross product can also be written in determinant form:

Some properties of the cross product: Figure The vector B x A equals –A x B.

Torque can be defined as the vector product of the force and the vector from the point of action of the force to the axis of rotation: Figure The torque due to the force F (in the plane of the wheel) starts the wheel rotating counterclockwise so ω and α point out of the page.

For a particle, the torque can be defined around a point O: Here, is the position vector from the particle relative to O. Figure τ = r x F, where r is the position vector.

Example 11-6: Torque vector. Suppose the vector is in the xz plane, and is given by = (1.2 m) + (1.2 m) Calculate the torque vector if = (150 N) . Solution: This can be done by the determinant method; the answer is τ = (180 m·N)j – it is in the y-direction, as expected.

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