## Introduction To Vector In Physics

Simply put, vectors are those physical quantities that have values as well as specific directions. Such as displacement, velocity, etc.

That is, you need to describe the direction of the quantity with the measurable properties of the physical quantity here.

For example, many of you say that the velocity of a particle is five. Since velocity is a vector quantity, just mentioning the value is not a complete argument. You need to specify the direction along with the value of velocity. So, you have to say that the value of velocity in the specified direction is five.

Graphically, a vector is represented by an arrow. Here, the vector is represented by ab. That is, the value of the given vector will depend on the length of the ab vector. And a is the initial point and b is the final point.

Analytically, a vector is represented by an arrow above the letter. And the value of the vector is always denoted by the mod

## Ap Physics C: Mechanics

AP Physics C: Mechanics is the equivalent of a calculus-based first-semester college physics course. It is most often taken over the course of an entire school year but, in high schools that offer block scheduling, can sometimes be taken during a single semester. This class covers kinematics, Newtons laws of motion, systems of particles and linear momentum, circular motion and rotation, oscillations and gravitation, and work, energy and power while using differential and integral calculus throughout the course.

The course also focuses heavily on science practices and as such, students spend a minimum of 20% of instructional time engaged in hands-on laboratory work.

There are no formal prerequisites for the class, but before taking AP Physics C: Mechanics, students should be prepared for college-level calculus-based work and must at minimum have taken or be concurrently taking calculus.

## Selected Solutions To Problems & Exercises

1. 4.09 × 1019 kg · m/s

3. 3.000000015 × 1013 kg · m/s Ratio of relativistic to classical momenta equals 1.000000005

5. 2.9957 × 108 m/s

7. 1.121 × 108 m/s The small speed tells us that the mass of a proton is substantially smaller than that of even a tiny amount of macroscopic matter!

- College Physics. : OpenStax College.
**Located at**: .**License**:*CC BY: Attribution*.**License Terms**: Located at License

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## Why So Many Ap Physics Classes

Up until 2014, the AP Physics 1 and AP Physics 2 courses were administered together under the title of AP Physics B. This original course covered all content from both courses but could not delve deeply into subject matter due to time constraints.

The division of this curriculum into AP Physics 1 and AP Physics 2 came after an evaluation of the curriculum by the College Board, in response to a 2002 study by the National Response Council, titled Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools.

This study formally recommended that a two-year sequence of advanced physics study replace Physics B, enabling students to delve deeper into key physics concepts as they develop the reasoning and inquiry skills necessary to think like scientists.

Re-designing the courses allows for deeper conceptual understanding and also aligns with a larger push in AP coursework to prioritize critical thinking and reasoning over memorization. Dividing the previous Physics B course allows more time to master foundational physics principles while engaging in science practices to earn credit or placement.

## Option : Ap Physics 1 Then Ap Physics C

**AP recommends Physics C for students aiming for engineering or physical science majors** in college. However,** taking AP Physics 1, Physics 2, and Physics C might be overkill**you would lose time taking other science courses, like biology and chemistry. Getting exposure to all three natural sciences is important for a well-rounded, challenging high school career, especially if you’re going into science or engineering. You also want to make sure you can fit in at least one of the AP Calculus classes.

So if you want to take Physics C, start with AP Physics 1 , and then take AP Physics C, which will give you a total of two physics classes during high school.

Physics C is intended as at least a second-year course, so don’t jump into it unprepared. Also make sure you have taken or are taking calculus while you take AP Physics C.

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## Ap Test Changes Due To Covid

**Due to the ongoing COVID-19 coronavirus pandemic, AP tests will now be held over three different sessions between May and June.** Your test dates, and whether or not your tests will be online or on paper, will depend on your school. To learn more about how all of this is going to work and get the latest information on test dates, AP online review, and what these changes means for you, be sure to check out our 2021 AP COVID-19 FAQ article.

## Importance Of Measurement In Physics:

When faced with questions like what is the distance of the sun from the earth, what is the speed of light, what is the mass of an electron, one realises the importance of measurement. From the very ancient time, the man started measuring different physical quantities by using conventional methods. His footsteps were used for measuring length while the shadow produced by the sun for measuring the time. But as science progressed, those types of measurements became inadequate. He introduced precise and well-defined methods for measuring different physical quantities, through which he reached to the perfection in measurements.

The measurement means the action of measuring something or measurement is defined as the process of determining the value of an unknown quantity by comparing it with some pre-defined standard.

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## Defining The Speed Of Light As An Explicit Constant

In 1983 the 17th meeting of the General Conference on Weights and Measures found that wavelengths from frequency measurements and a given value for the speed of light are more reproducible than the previous standard. They kept the 1967 definition of second, so the caesiumhyperfine frequency would now determine both the second and the metre. To do this, they redefined the metre as: “The metre is the length of the path traveled by light in vacuum during a time interval of 1/299792458 of a second.” As a result of this definition, the value of the speed of light in vacuum is exactly 299792458 m/s and has become a defined constant in the SI system of units. Improved experimental techniques that, prior to 1983, would have measured the speed of light no longer affect the known value of the speed of light in SI units, but instead allow a more precise realization of the metre by more accurately measuring the wavelength of Krypton-86 and other light sources.

## Vector Algebra In Physics

You all know that when scalar calculations are done, linear algebra rules are used to perform various operations. That is, when you do vector calculations, you have to perform different operations according to the vector algebra rule.

Vector algebra is a branch of mathematics where specific rules have been developed for performing various vector calculations. Vector calculation here means vector addition, vector subtraction, vector multiplication, and vector product. Also, equal vectors and opposite vectors are also a part of vector algebra which has been discussed earlier.

**You may have many questions in your mind that what is the difference between vector algebra and linear algebra?**

When you perform an operation with linear algebra, you only use the scalar quantity value for calculations. However, vector algebra requires the use of both values and directions for vector calculations.

So, vector algebra has five main rules

- Vector Addition
- Vector Multiplication
- Vector Division

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## Rewarding Careers In Physics:

A StFX Physics degree **opens many doors**. Students go on to become **successful research scientists** at universities and companies worldwide. They also have a **high rate of acceptance** into **medical and law schools**, and are superbly trained for a **career in education**, where science and math teachers are in **high demand**. A StFX Physics degree provides the quantitative critical thinking skills needed in many fields, and graduates find success in professions such as economics, environmental science, and engineering.

## The Parallel Between Gravity And Electrostatics

An electric field describes how an electric charge affects the region around it. It’s a powerful concept, because it allows you to determine ahead of time how a charge will be affected if it is brought into the region. Many people have trouble with the concept of a field, though, because it’s something that’s hard to get a real feel for. The fact is, though, that you’re already familiar with a field. We’ve talked about gravity, and we’ve even used a gravitational field we just didn’t call it a field.

When talking about gravity, we got into the habit of calling g “the acceleration due to gravity”. It’s more accurate to call g the gravitational field produced by the Earth at the surface of the Earth. If you understand gravity you can understand electric forces and fields because the equations that govern both have the same form.

The gravitational force between two masses separated by a distance r is given by Newton’s law of universal gravitation:

A similar equation applies to the force between two charges separated by a distance r:

The force equations are similar, so the behavior of interacting masses is similar to that of interacting charges, and similar analysis methods can be used. The main difference is that gravitational forces are always attractive, while electrostatic forces can be attractive or repulsive. The charge plays the same role in the electrostatic case that the mass plays in the case of the gravity.

F = mg

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## Cvode A Stiff/nonstiff Ode Solver In C

**10**

- 1a graduate student at Stanford University, Stanford, CA 94305
- 2a mathematician at Lawrence Livermore National Laboratory, Livermore, CA 94551

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## What Ap Physics Classes Are Offered

The AP Program used to offer three physics classes: AP Physics B, AP Physics C: Mechanics and AP Physics C: Electricity and Magnetism.

However**, the AP program recently replaced AP Physics B, a one-year course, with two one-year courses: AP Physics 1 and AP Physics 2.** These are both algebra-based physics courses, which means they don’t require a math background beyond Algebra II.

The AP program still offers AP Physics C, **which is broken into two courses and exams: Physics C: Mechanics and Physics C: Electricity and Magnetism.** Many schools teach these as the same class, or just teach one topic. Both of these courses are calculus-based.

This means that there are now four AP Physics exams:

- AP Physics 1
- AP Physics C: Electricity and Magnetism
- AP Physics C: Mechanics

**The fact that there are now four AP Physics exams** can be confusing. So do you take Physics 1, Physics 2, and Physics C in order? What’s new about Physics 1 and Physics 2? We will introduce you to all of the courses and help you decide which class is right for you.

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## Why Study Physics At Stfx

Youll learn in a department where faculty are dedicated to teaching and to their active research programs. Students receive a **world-class degree** in an environment where **questions are welcomed**, discussion encouraged, and opportunities presented to get **involved in research projects**, even after the first year. In the wider physics community, our students are authors on research publications and attend national and international physics conferences.

## Time Of Flight Techniques

A method of measuring the speed of light is to measure the time needed for light to travel to a mirror at a known distance and back. This is the working principle behind the FizeauFoucault apparatus developed by Hippolyte Fizeau and Léon Foucault.

The setup as used by Fizeau consists of a beam of light directed at a mirror 8 kilometres away. On the way from the source to the mirror, the beam passes through a rotating cogwheel. At a certain rate of rotation, the beam passes through one gap on the way out and another on the way back, but at slightly higher or lower rates, the beam strikes a tooth and does not pass through the wheel. Knowing the distance between the wheel and the mirror, the number of teeth on the wheel, and the rate of rotation, the speed of light can be calculated.

The method of Foucault replaces the cogwheel with a rotating mirror. Because the mirror keeps rotating while the light travels to the distant mirror and back, the light is reflected from the rotating mirror at a different angle on its way out than it is on its way back. From this difference in angle, the known speed of rotation and the distance to the distant mirror the speed of light may be calculated.

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## Advantages Of Si Units

The SI units of measurement system have several distinct advantages over all other systems in use. The main advantages of SI units are as follows:

- SI units are simpler than all other system of units.
- The SI units system is comprehensive.
*i.e.,*the seven base units of the SI system cover all branches of science, engineering and technology. - SI is a rational system of units.
*i.e.,*this system makes use of one unit for one physical quantity. - SI unit system is coherent.
*i.e.,*All the derived units can be easily obtained from fundamental and supplementary units through their multiplication or division. - The fundamental units of SI satisfy all the characteristics that a unit should have.
- SI unit system is a metric system.
*i.e.,*multiples and submultiples of the units can be easily expressed as powers of 10. - SI units are internationally accepted.

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## Upper Limit On Speeds

According to special relativity, the energy of an object with rest mass*m* and speed *v* is given by *mc*2, where is the Lorentz factor defined above. When *v* is zero, is equal to one, giving rise to the famous *E* = *mc*2 formula for massenergy equivalence. The factor approaches infinity as *v* approaches *c*, and it would take an infinite amount of energy to accelerate an object with mass to the speed of light. The speed of light is the upper limit for the speeds of objects with positive rest mass, and individual photons cannot travel faster than the speed of light. This is experimentally established in many tests of relativistic energy and momentum.

## The Law Of Conservation Of Charge

The Law of conservation of charge states that the net charge of an isolated system remains constant.

If a system starts out with an equal number of positive and negative charges, there¹s nothing we can do to create an excess of one kind of charge in that system unless we bring in charge from outside the system . Likewise, if something starts out with a certain net charge, say +100 e, it will always have +100 e unless it is allowed to interact with something external to it.

Charge can be created and destroyed, but only in positive-negative pairs.

Table of elementary particle masses and charges:

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## Misconception Alert: Relativistic Mass And Momentum

The relativistically correct definition of momentum as *p* = *mu* is sometimes taken to imply that mass varies with velocity: *m*var = *m*, particularly in older textbooks. However, note that *m* is the mass of the object as measured by a person at rest relative to the object. Thus, *m* is defined to be the rest mass, which could be measured at rest, perhaps using gravity. When a mass is moving relative to an observer, the only way that its mass can be determined is through collisions or other means in which momentum is involved. Since the mass of a moving object cannot be determined independently of momentum, the only meaningful mass is rest mass. Thus, when we use the term mass, assume it to be identical to rest mass.

Relativistic momentum is defined in such a way that the conservation of momentum will hold in all inertial frames. Whenever the net external force on a system is zero, relativistic momentum is conserved, just as is the case for classical momentum. This has been verified in numerous experiments.

In Relativistic Energy, the relationship of relativistic momentum to energy is explored. That subject will produce our first inkling that objects without mass may also have momentum.

## What Are Vectors In Physics

A physical quantity is a quantity whose physical properties you can measure. Such as mass, force, velocity, displacement, temperature, etc.

Suppose you are told to measure your happiness. In this case, you can never measure your happiness. That is, you cannot describe and analyze with measure how much happiness you have. So, happiness here is not a physical quantity.

Suppose you have a fever. And the doctor ordered you to measure your body temperature. Then you measured your body temperature with a thermometer and told the doctor. When you tell your doctor about your body temperature, you need to use the word degree centigrade or degree Fahrenheit.

So, the temperature here is a measurable quantity. So we will use temperature as a physical quantity.

In general, we will divide the physical quantity into three types

In this tutorial, we will only discuss vector quantity. But before that, lets talk about scalar.

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