What Is Inertia Of Motion
From Newtons first law of motion, it is clear that a body has a tendency to remain at rest or in uniform motion. This property of the body is known as inertia. Thus inertia is that property of a body due to which it opposes or resists any change in its state of rest or uniform motion.
The term inertia may be referred to as the amount of resistance of an object to a change in velocity or resistance to change in motion. This includes changes in the speed of the object or the direction of motion. One aspect of this property is the tendency of things to continue to move in a straight line at a constant speed, when no forces are affecting them.
There are Two Numerical Measures of the Inertia of a Body:
1- The Body Mass:
which governs its resistance to the action of a force.
Mass is the measure of inertia of the body i.e., greater the mass, greater will be inertia. Thus inertia of a body depends upon its mass.
That is, massive objects possessed more inertia than lighter ones. E.g., Mass of a stone is more than a mass of a rubber ball for the same size. Therefore, the inertia of the stone is more than that of a rubber ball.
The inertial mass is a measure of the tendency of an object to resist acceleration. The more mass something has, the more it resists acceleration.
There is also gravitational mass, which as far as we can tell experimentally is identical to inertial mass.
2- The Body Moment of Inertia about a Specified Axis:
Class 11 Physics Chapter 7 System Of Particle And Rotational Motion
In linear motion, we have linear velocity. Analogues to this, in rotational motion we have angular velocity. In the same manner, in this article, we will find analogue to mass in rotational motion. Lets talk about moment of inertia, an analogue to mass in rotational motion.If we consider rigid body about a fixed axis then angular speed of body is . Let ith be the particle of body having mass mi rotating in circular path of radius ri. Therefore, the linear velocity of ith particle can be given asvi= ri.
Kinetic energy of ith particle isKi= ½ mivi2 It means that kinetic energy of whole body is sum of kinetic energies of i particlesTherefore, K = Ki = Therefore, Ki = ½ 2)since vi = ri Ki = ½ as, 2 is constantTherefore Ki = ½ ) 2The term signifies moment of inertia denoted by I. i.e. I = Therefore, K = ½ I 2 Now compare equation and equation , it an be seen that moment of inertia I is the analogue of mass in rotational motion.
Newton’s First Law Of Motion And Inertia
Isaac Newton developed the principles shown in Galileo’s observations into his first law of motion. It takes a force to stop the ball from continuing to roll once it is set in motion. It takes a force to change its speed and direction. It doesn’t need a force to continue moving at the same speed in the same direction. The first law of motion is often referred to as the law of inertia. This law applies to an inertial reference frame. Corollary 5 of Newton‘s Principia says:
The motions of bodies included in a given space are the same among themselves, whether that space is at rest or moves uniformly forwards in a straight line without circular motion.
In this way, if you drop a ball on a moving train that is not accelerating, you will see the ball fall straight downward, as you would on a train that was not moving.
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Inertia Varies With Mass
According to Newton’s Second Law, the force required to change the state of motion of an object is the product of the object’s mass and the acceleration produced by the force :
F = ma
To understand how mass is related to inertia, consider a constant force Fc acting on two different bodies. The first body has mass m1 and the second body has mass m2.
When acting on m1, Fc produces an acceleration a1:
m1/m2 = a2/a1
If m1 is bigger than m2, then you know a2 will be bigger than a1 to make both equal Fc, and vice versa.
In other words, the mass of the object is a measure of its tendency to resist the force and continue in the same state of motion. Although mass and inertia don’t mean exactly the same thing, inertia is usually measured in units of mass. In the SI system, its units are grams and kilograms, and in the British system, the units are slugs. Scientists usually don’t discuss inertia in motion problems. They usually discuss mass.
What Is The Inertia Law
Newton’s first law of motion, usually known as the law of inertia, asserts thatunless an external force acts on an object, it will remain in either a condition of rest or motion. We have all heard of the Aristotle fallacy, which states that a body must always be propelled by an external force. When the concept of inertia was introduced, this was shown to be incorrect. Galileo discovered the notion of inertia with the following two tests.
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Calculating Moment Of Inertia
The graphic on this page shows an equation of how to calculate the moment of inertia in its most general form. It basically consists of the following steps:
- Measure the distance r from any particle in the object to the axis of symmetry
- Square that distance
- Multiply that squared distance times the mass of the particle
- Repeat for every particle in the object
- Add all of these values up
For an extremely basic object with a clearly-defined number of particles , it’s possible to just do a brute-force calculation of this value as described above. In reality, though, most objects are complex enough that this isn’t particularly feasible .
Instead, there are a variety of methods for calculating the moment of inertia that are particularly useful. A number of common objects, such as rotating cylinders or spheres, have a very well-defined moment of inertia formulas. There are mathematical means of addressing the problem and calculating the moment of inertia for those objects which are more uncommon and irregular, and thus pose more of a challenge.
Importance Of Inertia In Our Daily Life
The inertia of an object enables us to maintain patterns of functioning, maintain relationships, and get through the day without questioning everything. It has many important uses:
- The design of safety devices for vehicles, including but not limited to seat belts, that can provide an external force to stop a bodys motion in the event of a sudden change in the physics of the immediate environment.
- In space travel, for example, once a device escapes Earths gravity, it will continue on its given trajectory until it encounters another gravitational field or object.
- Space probes can be sent great distances without any additional fuel required other than that needed to escape Earth, enact minor navigational changes or land on another object.
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Using Moment Of Inertia
The moment of inertia of an object rotating around a fixed object is useful in calculating two key quantities in rotational motion:
- Angular Momentum:L = IÏ
You may notice that the above equations are extremely similar to the formulas for linear kinetic energy and momentum, with moment of inertia “I” taking the place of mass “m” and angular velocity “Ï” taking the place of velocity “v,” which again demonstrates the similarities between the various concepts in rotational motion and in the more traditional linear motion cases.
Inertia: The Force That Holds The Universe Together
Inertia is the force that holds the universe together. Literally. Without it, things would fall apart. Its also what keeps us locked in destructive habits, and resistant to change.
If it were possible to flick a switch and turn off inertia, the universe would collapse in an instant to a clump of matter, write Peter and Neal Garneau in In the Grip of the Distant Universe: The Science of Inertia.
death is the destination we all share. No one has ever escaped it. And that is as it should be, because death is very likely the single best invention of life. Its lifes change agent it clears out the old to make way for the new Your time is limited, so dont waste it living someone elses life.
Inertia is the force that holds the universe together. Literally. Without it, matter would lack the electric forces necessary to form its current arrangement. Inertia is counteracted by the heat and kinetic energy produced by moving particles. Subtract it and everything cools to -459.67 degrees Fahrenheit . Yet we know so little about inertia and how to leverage it in our daily lives.
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Significance Of Moment Of Inertia
- In rotational motion inertia of body resist the change in its state of rest or motion with a uniform angular velocity. Say that body is rotating with constant angular velocity. Change the rotational motion by applying torque in direction of motion or in opposite direction of motion. It body require large torque to change its shape then body posses greater inertia. This suggest that moment of inertia is greater about the axis of rotation.
- Mass is independent but moment of inertia is not a fixed quantity. However, it depends on
- Mass of the body
- Shape and size of the body
- Distribution of mass about the axis of rotation
- Position and orientation of axis of rotation
Inertia Of Rest Examples
Now that you know what inertia of rest is, explore several examples.
- If pulled quickly, a tablecloth can be removed from underneath the dishes. The dishes have the tendency to remain still as long as the friction from the movement of the tablecloth is not too great.
- If a stopped car is hit by a moving car from behind, the passengers inside may experience whiplash as a result of the body moving forward but the head lagging behind. The head is experiencing inertia.
- A balloon in a car will appear to move when the car moves forward, but the balloon is actually attempting to stay in the place it was, it is only the car that is moving.
- When a car is abruptly accelerated, drivers and passengers may feel as though their bodies are moving backward. In reality, inertia is making the body want to stay in place as the car moves forward.
- If an index card is placed on top of a glass with a penny on top of it, the index card can be quickly removed while the penny falls straight into the glass, as the penny is demonstrating inertia.
- When pulling a Band-Aid off, it is better to pull it fast. Your skin will remain at rest due to inertia, and the force pulls the Band-Aid off.
Objects in motion stay in motion or want to, just like these examples.
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Galileo And The Inertia Concept
The concept of inertia was created by Galileo, a leading scientist in the seventeenth century. According to Galileo, moving objects eventually come to a standstill due to a force known as friction. Galileo found that a ball would roll down one plane and up the opposite plane to roughly the same height in tests utilising a pair of inclined planes facing each other. The ball would roll up the opposite plane even closer to the original height if smoother planes were utilised. Any difference between the initial and final heights, Galileo reasoned, was attributable to friction. Galileo claimed that if friction were fully removed, the ball would soar to the exact same height.
What Are The Types Of Moment Of Inertia Units
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How Did Galileo Explain Inertia
Galileo hypothesized that a falling object gains an equal amount of velocity in equal intervals of time. This also means that the speed increases at a constant rate as it falls. But, there was a problem in testing this hypothesis: it was impossible for Galileo to observe the objects free-falling motion and at the time, technology was unable to record such high speeds. As a result, Galileo attempted to decelerate its motion by replacing the falling object with a ball rolling down an inclined plane. Since free-falling is basically equivalent to a completely vertical ramp, he assumed that a ball rolling down a ramp would speed up in the exact same way as a falling ball would.
Using a water clock, Galileo measured the time it took for the rolling ball to reach a known distance down the inclined plane. After several trials, it was observed that the time it took for the ball to roll the entire length of the ramp was equal to double the amount of time it took for the same ball to only roll a quarter of the distance. In short, if you were to double the amount of distance the ball traveled, it would travel four times as far. Through this experiment, Galileo concluded that
If an object is released from rest and gains speed at a steady rate , then the total distance traveled by the object is proportional to the time squared needed for that travel.
Mathematically, this is expressed as
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The Inertia Of Direction Examples
A few Real-life Examples are discussed below:
A bike tends to move in a straight line unless we turn the handle on the bike.
You use umbrellas to prevent yourself from getting wet. The direction of the raindrops is vertically downwards.
They cannot change their direction to make you wet.
When you spin the one end of a string tied to the stone. Suddenly the string breaks and stoneflies off along the tangent to the circle. This is because the pull in the string was forcing the stone to make a circular motion.
As soon as the string breaks, the pull vanishes, and the stoneflies off tangentially.
Status Quo Bias: When In Doubt Do Nothing
Cognitive inertia also manifests in the form of status quo bias. When making decisions, we are rarely rational. Faced with competing options and information, we often opt for the default because its easy. Doing something other than what were already doing requires mental energy that we would rather preserve. In many areas, this helps us avoid decision fatigue.
Many of us eat the same meals most of the time, wear similar outfits, and follow routines. This tendency usually serves us well. But the status quo is not necessarily the optimum solution. Indeed, it may be outright harmful or at least unhelpful if something has changed in the environment or we want to optimize our use of time.
The great enemy of any attempt to change mens habits is inertia. Civilization is limited by inertia.
Edward L. Bernays, Propaganda
Simple Examples Of Moment Of Inertia
How difficult is it to rotate a particular object ? The answer depends on the shape of the object and where the object’s mass is concentrated. So, for example, the amount of inertia is fairly slight in a wheel with an axis in the middle. All the mass is evenly distributed around the pivot point, so a small amount of torque on the wheel in the right direction will get it to change its velocity. However, it’s much harder, and the measured moment of inertia would be greater, if you tried to flip that same wheel against its axis, or rotate a telephone pole.
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A Detailed Discussion Of The Law Of Inertia
Newton’s first law of motion is also cited as the law of inertia.
This law states that a body continues to be in the state of rest or uniform motion along a straight line unless it is acted upon by an external force to change its state.
In our daily life, we find that a ball rolling on the ground stops after some time. This is because the frictional force of the ground is acting upon the ball to make changes in its state of motion.
The inertia of a body is measured by the mass of the body.
Heavier is the mass, greater is the force required hence, greater is its inertia and vice-versa.
Hence, Newtons first law defines inertia, and it is justly called the law of inertia.
Theories Of Motion From Aristotle To Galileo
In everyday life, we see rolling balls come to rest. But they do so because they are acted on by force of gravity and from the effects of friction and air resistance. Because that is what we observe, for many centuries Western thought followed the theory of Aristotle, who said that moving objects would eventually come to rest and needed continued force to keep them in motion.
In the seventeenth century, Galileo experimented with rolling balls on inclined planes. He discovered that as friction was reduced, balls rolled down an inclined plane attained almost the same height rolling back up an opposing plane. He reasoned that if there were no friction, they would roll down an incline and then keep rolling on a horizontal surface forever. It wasn’t something innate in the ball that caused it to stop rolling it was contact with the surface.
What Is Inertia In Physics
Inertia Definition Physics :The property of an object by virtue of which it cannot change its state of rest or of uniform motion along a straight line on its own, is called inertia. Greater the mass of a body greater will be its inertia and vice-versa.
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