Tag: Velocity

Introduction

In physics, there are two types of physical quantities: those that contain a direction as well as magnitude and those that contain only direction. The former are known as vector quantities and the latter are known as scalars. Time, temperature, mass, etc. are scalar quantities since there is no physical sense for mass to have direction. On the other hand, velocity, acceleration, force, etc. are quantities whose directions are important and thus, are examples of vectors.

The process of determining the magnitude and where applicable, the direction of a quantity is known as measurement. It yields a numerical value along with a direction if required. Measuring quantities also requires a standard set of units with reference to which, we can give their numerical value. For instance, we know our height to be 160 cm only because we have a reference value for how long 1 cm is. For this end, the SI system of units was developed to provide a global standard.

What is speed?

Speed measures the pace at which an object moves with reference to a reference point. When we talk of speed in physics, we are concerned with only the distance covered and do not inquire about the direction. Thus, speed is a scalar quantity. Mathematically, we can write:

In the SI system of units, speed is measured in m/s whereas the cgs system measures it in cm/s. Other common units include km/h, mph, etc.

Apart from moving in a straight path, objects can also move along a circular path in which case, we can measure their angular speed in terms of the angle they sweep out in a given time interval. Mathematically,

Types of speed

Physicists classify speed into various types depending on different criteria. Here are a few common classifications:

Uniform speed

An object is said to possess uniform speed if the speed remains constant in time. That is, even as time passes, its speed does not change.

Variable speed

Objects whose speed is not constant in time are said to be moving with a variable speed.

Average speed

We know that it is practically difficult for objects to keep moving at exactly the same speed over time. But over the course of a journey, one can calculate an average speed which gives us a general idea about the motion of the object. 

Average speed is measured by taking the total distance that the object covered and dividing it by the total time it took to cover that distance. That is,

Instantaneous speed:

As previously mentioned, an object may have different speeds at different instants in time. The value of its speed at an exactly defined moment in time is termed as its instantaneous speed at that moment.

The calculation for speed

To calculate an object’s speed, we can simply apply the formula for speed. Thus,

A few common examples of speeds measured by scientists include the speed of light in vacuum, which is approximately 3E8 m/s. On the other hand, the speed at which Earth rotates about its axis is 7.28E-5 rad/s and the speed at which it travels around the sun is given as 30 km/s.

Relation between angular speed and linear speed

We can derive a relation between the angular and linear speeds of an object. We know that linear speed is 

Further, we know that for circular motion, when the angle swept is very small, the arc length can be approximated as 

The angular speed is written as ⍵=θ/t. Hence, if we multiply both sides of this equation with r, we get:

Thus, angular and linear speeds are related by the equation v=r.

Solved examples

1. Raju drives at 15 km/h for 3 hours. How much distance did he cover?

We know that 

2. If the blade of a fan rotates at an angular speed of 16π rad/sec, what is the time taken for one complete rotation.

Angular speed can be directly related to the time taken for one complete rotation (T) as follows:

Hence, the fan completes one rotation in 0.125 seconds.

Summary

Speed is a scalar quantity that measures the pace at which an object is moving. It is measured by dividing the distance covered by the time taken to cover that distance. Angular and linear speeds can be related to each other.

Frequently asked questions

1. Describe Newton’s first law of motion.

Newton’s first law states that if an object is moving or at rest, it will continue in that state unless some external factor forces it to change its state of motion. Unless some external factor stops a ball from rolling, it will continue rolling.

2. How does the angular speed of an object remain the same at all points?

Angular speed measures the rate at which a certain amount of angle is swept by an object. It changes with radius and thus, remains the same for all points.

3. How does an ice skater control their angular speed?

Since angular speed depends on the radius, if the ice skater or ballet dancer pulls in their arm close to their body, they speed up. They can also reduce their speed by extending their arms. This is related to the law of conservation of angular momentum.

4. What instrument measures linear and angular speeds?

Linear speed is measured by speedometer in a car while angular speed is measured by an instrument known as tachometer.

5. What is the difference between speed and velocity?

Introduction

A wave is defined as the propagation of a continuous disturbance across two points. They can propagate with, or without a medium in between the given points and on this basis, they are broadly classified as follows:

1. Mechanical waves: A wave that requires a medium to propagate. For sound waves cannot travel in vacuum.
2. Electromagnetic waves: These waves need no medium to travel and thus, can travel in vacuum as well. Light is a common example of electromagnetic waves. They can also be defined as a pulse of energy that traverses through vacuum or a given medium.

Waves generally travel in the form of crests and troughs and are characterised by  various factors like amplitude, velocity, frequency, etc. In simple terms, the amplitude is a measure of the energy they carry. 

Define the Amplitude of a wave

The amplitude of a wave is a measure of the energy transferred by it and is defined as the distance from the axis to the bottom or top of a peak or valley of the wave. Generally, this value is expressed in metres (m), though other measurements exist as well.  Amplitude determines how much the wave rises and falls and waves with higher amplitudes carry more energy than those with lower ones. 

Mathematically, a sinusoidal wave can be represented by the following equation:

We can define amplitude in another way. It can be understood that the amount of displacement of a particle in the wave is an indication of the energy required to create its motion. This quantity of energy is expressed as the amplitude of the wave.

Sound

Sound is a form of energy that causes objects to vibrate. It can be transferred across two locations through a medium that may be solid, liquid, or gas.  Sound waves are longitudinal in nature and thus, move in the form of compressions and rarefactions. When an object produces sound, its vibrations transfer energy to the molecules of the medium around it, which then propagate and reach our eardrums. Our ears convert these vibrations into signals that our brain can interpret as sound.  The range of sound frequencies audible to humans is 20Hz to 20KHz, and frequencies above and below this range are known as ultrasound and infrasound, respectively. 

Ultrasound waves

Ultrasonic waves mostly find use in the medical field in the diagnosis of various diseases. Processes like ultrasonography utilize ultrasounds.

Infrasonic waves

These are sound waves with frequencies below the 20 Hz mark, which are generally produced in natural phenomenon like volcanic eruptions, earthquakes, etc.

Define Amplitude in Physics?

In physics, amplitude refers to the maximum distance or displacement travelled by a vibrating body or wave from its resting point. All waves possess an amplitude and it is an important characteristic that defines waves. 

Amplitude modulation is a technique used to modulate the amplitude of a given wave.  Generally, a low amplitude wave is modulated using a carrier wave. This process allows us to transmit data across locations. Amplitude modulation has several applications such as signal transmission, radio broadcasting among others.

Characteristics of Sound

• Pitch: Pitch refers to the subjective sensation of the frequency of a sound wave. A high-frequency sound wave produces a high pitched sound, while a low-frequency sound wave produces a low pitched sound. Pitch or frequency is measured in Hertz (Hz).
• Loudness: The loudness of sound is determined by the amplitude or size of the sound wave. A larger size or amplitude corresponds to a louder sound. Loudness is measured in decibels (dB).
• Amplitude: Amplitude is the maximum displacement of the particles from their mean position as sound waves travel through the medium. It is expressed in metres.
• Wavelength: Sound is a longitudinal wave and it travels across two points via a medium in the form of compressions and rarefactions. It is characterised by a certain wavelength, which is defined as the distance between two consecutive compressions or rarefactions. Typically, these wavelengths lie between 1.7 cm to 17 metres. 

Wavelength is connected to speed and frequency of sound via the following relation:

  \[\lambda  = \frac{v}{f}\]

• Frequency: The number of compressions or rarefactions that a sound wave produces in unit time is known as the frequency of the wave. It is expressed in Hertz (Hz), which is equal to one second inverse.

  \[f = \frac{1}{T}\]   

• Time period: The time taken for the particles of the medium to undergo a complete cycle from one compression to the next is known as the time period. Time period and frequency are inversely related. Its unit is second.

\[T = \frac{1}{f}\] 

• Velocity: The velocity of the wave measures how fast the disturbance in the medium travels between two locations. It can vary depending on the medium in question and is expressed in (\(m{s^{ – 1}}\))

  Velocity=Displacement/ time

Summary

Waves are a common phenomenon that we encounter in our day-to-day lives. For instaande , the light waves produced by the sun, the waves in the ocean, and the sound waves we hear. In terms of physics, waves are a way of transferring energy via a disturbance. 

Sound waves are generated by a vibrating body that transfers energy to the molecules of the medium that surrounds it. This energy in the form of vibration then propagates through the medium. Sounds can take many forms, such as pleasant sounds, noise, music, etc. Understanding the characteristic properties of sound waves is essential for the creation of music and for other applications.

 

Frequently Asked Questions

1. State the differences between pitch and loudness?

2. Are pitch and frequency different?

Frequency is a measure of how often a particular event occurs whereas pitch is a concept that is closely related to frequency. Even though the two properties are related, there is no mathematical relation for the same. 

Note that while frequency is relevant for all types of waves, including mechanical and electromagnetic waves, the pitch is a challenging concept to define and is relevant only for sound waves.

3. What is the hearing range of the human ear?

Sound waves in the 20 Hz to 20,000 Hz regime are audible to the human ear. It might be interesting to note that while some newborns can hear slightly above the 20 kHz mark, but they lose this sensitivity with age.

4. What is the relation between wavelength, velocity, and frequency of a wave?

\[v = f\lambda \]

From the above relation, it is evident that wavelength and frequency are inversely related. Note that the frequency of a wave never changes. The velocity and wavelength increase or decrease in different media.

5. What are the three ways in which the above equation can be written?

Introduction

An engine used to convert mechanical energy into electrical energy is an AC generator. Steam turbines, gas turbines, water turbines, and other similar devices all generate this energy. It creates a sinusoidal waveform of alternating current. Alternators are another name for AC generators. The electromagnetic induction law of Faraday is the foundation of an AC generator. According to this rule, anytime a conductor is exposed to a variety of magnetic fields, an electromotive force (EMF) is generated across it. This EMF is referred to as an induced EMF. Electromagnetic induction is the term for this phenomenon. Induced electromagnetic induction is the process by which a coil develops a potential difference as a result of changes in the magnetic flux flowing through it. Several types of AC generators, including polyphase generators, rotating field generators and spinning armature generators.

For more details watch the video of the Science Course for classes 6th, 7th, and 8th.

What is an AC Generator?

An AC generator is an engine that converts mechanical energy into electrical energy in the form of an alternating driving force. To provide a consistent magnetic field, an AC generator uses two magnet poles.

AC Generator Parts and Function

An electromagnet with two poles, the North Pole and the South Pole, is a component of an AC generator.  Below is a discussion of certain AC generator components, including the rotor, slip rings, and armature loop.

a. Field

The output voltage of an AC generator is obtained from the source using conductor loops. The field’s main function is to provide a magnetic field that will stimulate the gadget.

b. Armature

The armature coil is a coil that is part of the generator and produces output voltage. An armature coil’s job is to move electricity through the generator.

c. Prime Mover 

The primary mover of an AC generator is either an engine or a turbine. It serves as the appliance’s power supply.

d. Rotor 

A rotor is a revolving component with magnetic field spirals. It generates the necessary output voltage.

e. Stator

A stationary part holding the armature spirals is called a stator. A stator includes three different parts. They are stator frame, stator core, and armature spirals.

1. Stator frame: A frame that grips the stator core and armature spirals.
2. Stator core: There are slots in the inner part of the core that hold the armature spirals. A steel or iron is coated on the walls of the stator core to decrease the eddy current losses.
3. Armature winding: They are bounded on the stator core.

f. Slip Rings

There are two small rectangular blocks fixed with slip rings called carbon brushes. They are attached to the galvanometer.

Principle of Electric Generator

The basis of AC generators is Faraday’s law of electromagnetic induction. A current-carrying coil placed in a consistent field of force produces the driving force that is referred to as the law.

Construction and Working of an AC Generator 

An AC generator consists of a rectangular coil with two magnet poles attached to it on either side. Two rings are used to fasten the coil’s (or loop’s) perimeter. The rings are joined together with brushes. When a conductor travels in a magnetic field, an electric 

The generator induces a current in it.

Between the magnet’s poles, a rotating rectangular coil, also known as an armature, is used. The magnetic field’s vertical axis is the centre of rotation. The flux in contact with the armature changes as it rotates constantly. The alteration in flux results in the generation of an emf. As a result, the galvanometer, slip rings, and carbon brushes produce an electric current. While direct current only travels in one direction, alternating current sometimes flips direction.

The production of the AC generator shown in the above graph is described as

1. Induced EMF is zero when the coil is at point A because it moves equidistantly from the magnetic field’s curve at that point.
2. A gradient of 90o is created between the coil‘s motion and the magnetic field as it moves from point A to point B, and induced EMF is at its highest level during this time.
3. Moving the coil from A to B results in the same motion being equally far from the magnetic field and no generated EMF.
4. The induced EMF is once more at its highest when the coil is moved from C to D since its motion is antiparallel to the magnetic field and its angle is 270o.
5. The coil completes one cycle and moves equally far from the magnetic field when it moves from D to A. Induced EMF is therefore zero.

Advantages of AC Generator Over DC Generator

Category	AC Generator	DC Generator
Output Voltage	Higher Output Voltage.	It cannot generate a higher output voltage as it damages the functioning of the commutator.
Construction	Simpler construction	Construction is complicated due to a commutator.
Functioning	Works on the principle of electromagnetic induction.	DC generator functioning is more complex than an AC generator.
Maintenance	It demands less maintenance.	It demands more maintenance than an AC generator.
Cost	Cheaper	Costs higher than AC generator
Efficiency	Transmission efficiency is higher as AC reduces transmission losses.	Transmission efficiency is lower.

You can also read “What is AC Voltage Capacitor?” for explanation of AC voltage.

Summary

A generator is an engine that changes one type of energy into another. Large currents are produced by electric generators for usage in industrial and domestic applications. There are two different kinds of electric generators: DC generators, which convert mechanical energy into direct current. A generator of alternating current that converts mechanical energy. On the Faraday law of EMI theory, an AC generator was placed. In an AC generator, the flux in contact with the armature varies as it rotates continuously. The shift in flux causes an emf to be generated. As a result, the galvanometer, slip rings, and carbon brushes produce an electric current. As an AC generator produces higher output voltage, it is easier to build, requires less maintenance, is more efficient, and is less expensive than a DC generator. Large currents are produced by electric generators for usage in industrial and domestic applications.

Frequently Asked Questions 

1. Can we Generate EMF without Rotating the Coil in an AC Generator? Explain.

Ans: Yes, emf may be produced without the coil revolving. If the armature is made to move at a velocity perpendicular to the magnetic field, Emf can also be produced.

2. What is the reason for Heat Loss in the Generator?

Ans: Reasons for the heat loss in the generator can be, (a) generation of the by-products like carbon dioxide, and molecular friction, which can reduce the efficiency. The heat loss hinders the efficiency of the generator. So, the efficiency is never 100%. 

3. What is the Driving Force?

Ans: Induced emf is also termed as the driving force and can be expressed as, 

                                                      ε = N B Aωsinωt

where N is the number of turns in the coil, B is a magnetic field, A is an area, ω is the angular velocity

So, in an AC generator, the induced emf is proportional to the applied magnetic field.

4. Give examples of DC Sources.

Ans: The electrical appliances like radios, televisions, and solar panels. DC only travels in one direction and lacks any polarity.

Introduction

The rate of change in displacement of a moving object is referred to as its velocity. As a result, velocity is a vector quantity, and the velocity-time graph or velocity-time relation is a graphical representation of its fluctuation with time. A velocity-time graph shows the variation of the object’s velocity with time, under different conditions, such as under uniform motion, and under acceleration. On a velocity-time graph, acceleration is depicted by the slope of the graph line.

Velocity-Time Graph for Uniform Motion (No acceleration)

Since there is no acceleration being given to the moving object in this scenario, its velocity is constant and does not fluctuate over time. As a result, in this scenario, it is clear from Figure (a) below that despite the change in time, the velocity will remain constant throughout the entire journey of the object.

Velocity-Time Graph with a Constant Uniform Acceleration

In this situation, the item is subject to a constant uniform acceleration, so depending on the applied uniform acceleration—referred to as the accelerating and retarding acceleration, respectively—its velocity will constantly grow or decrease. We see a linear behaviour of the object’s velocity with time in the velocity-time graph (as shown below in Figure (b)), where the velocity of the item grows linearly on the application of constant uniform acceleration. You can use the slope of this graph to calculate the object’s applied acceleration.

The object’s equations of motion under a uniform constant acceleration can be expressed as follows:

v = u + at

s = ut + 1/2 at²

v² = u² + 2as

Where v, u, a, s, and t are the final velocity, initial velocity, uniform acceleration, total displacement of the object, and travel/trip time, respectively.

Velocity-Time Graph under a Variable Acceleration

As shown in Figure (c) above, in this situation, the acceleration acting on the object varies with time and as a result, the object’s variation in velocity is different during each time period of the journey. As a result, we observe a velocity-time graph that differs from the case where the object is subjected to variable acceleration and observe a parabolic behaviour of velocity with time.

Summary

The rate of change of displacement is known as velocity. The slope of the curves on the velocity-time graphs indicates how quickly the item is accelerating. Any object’s velocity is determined by the rate at which its displacement changes, so its starting and ending positions are crucial.

Frequently Asked Questions

1.What is the Initial and Final Velocity?

Ans: An object’s initial velocity is its speed at time zero, or when it first begins moving, and its final velocity is its speed when the journey has come to an end.

2. State the difference and Similarity between Speed and Velocity.

Ans: The pace at which a distance changes is known as an object’s speed, whereas the rate at which its displacement changes is known as its velocity. Speed and velocity are scalars and vector quantities because distance and displacement are, respectively, scalar and vector quantities. Since both distance and displacement are expressed in meters, there is an m/s correspondence between speed and velocity.

3. What are the differences between Velocity and Acceleration?

Attributes	Velocity	Acceleration
Definition	The speed of an object in a given direction.	Acceleration implies any change in the velocity of the object with respect to time.
Calculated with	Displacement.	Velocity
What is it?	Rate of change of displacement.	Rate of change of velocity.
Formula	Displacement/Time	Velocity/Time
Unit of Measurement	Meter/Second	Meter/second²

4. What do Velocity Time Graphs Show?

Ans: A velocity-time graph displays the sprinter’s object’s changing speed, as well as the speed of any other moving item or person. The slope of the graph line on a velocity-time graph is used to illustrate acceleration. If the line slopes downhill, as it does between 7 and 10 seconds, then acceleration is negative, and velocity is dropping.