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Difference between Momentum and Inertia is that inertia is the resistance of a body to the motion, while momentum is where a body tends to continue moving. Momentum is inertia in motion and is defined as the product of the mass of an object and the velocity of the object. Inertia is the inability of an object to change its state of rest or motion/move in a particular direction by itself.
- There are three types of inertia, Inertia of rest, Inertia of motion and Inertia of direction.
- The terms inertia and momentum are frequently confused, partly because their definitions are similar.
- While inertia is a critical sizing characteristic, momentum isn't directly handled in system calculations.
- The main difference between momentum and inertia is that momentum is a measure of the amount of motion that an object possesses, while inertia is a measure of the object's resistance to any change in its state of motion.
Read Also: Unit of Momentum
| Table of Contents |
Key Terms: Inertia, Momentum, Law of Inertia, Motion of Inertia, Angular Momentum, Velocity, Mass, Conservation of Energy, Inertia of Rest, Scalar Quantity, Vector Quantity
What is Inertia?
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Inertia is the resistance of a body to change its speed, and it is proportional to its mass and distance from the axis of rotation. A skater spinning on the ice is a classic representation of inertia.
Because a portion of her mass is far from the axis of rotation while her arms are outstretched, she spins at a “sluggish” rate. However, as she draws her arms closer to her body, her rate of spin increases since her total mass is now near the rotation axis.
The formula of Inertia is
| I = mr2 |
Where, I is the mass moment of inertia (kgm2 or lbft2), m is the mass (kg or lb), and r is the rotation axis distance (m or ft).
- Inertia is a property of matter that describes the resistance of an object to changes in its state of motion.
- It is a fundamental concept in physics and is related to the mass of an object.
- The greater the mass of an object, the greater its inertia.
- Inertia is a measure of the "sluggishness" of an object.
- An object at rest will tend to remain at rest unless acted upon by an external force.
Laws of Motion Video Lecture
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Types of Inertia
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The various types of inertia are:
Inertia of Rest
Inertia of rest refers to a body's incapacity to change its state of rest on its own. Example: When a car begins, a person seated in the car falls backwards. Because of the inertia of rest, the lower component of the car begins to move while the top portion seeks to remain stationary.
Inertia of Motion
Inertia of motion refers to the body's incapacity to change its state of motion on its own. Example: A person sitting in a car, falls forward when the car hits the brakes. Because of inertia of motion, the lower component of the car comes to a stop while the higher portion continues to move.
Inertia of Direction
A body's incapacity to change its direction of motion on its own. Example: Because of the inertia of motion, a person seated inside an automobile is thrown outwards in order to maintain his direction of motion.
What is Momentum?
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Momentum is defined as the product of an object's mass and velocity. It is also known as "mass in motion." While a change in shape can modify a system's inertia, it cannot change its momentum until an external force acts on it. The conservation of momentum is the name for this principle.
A game of billiards is a typical illustration of momentum. Consider the collision of a moving ball, such as a cue ball, with a stationary ball. The momentum of the cue ball has been totally transferred to the second ball when it stops travelling (v = 0). If both balls move as a result of the collision, the cue ball's momentum is shared between the two balls.
A linear system's momentum equation is simply P = mv, where P = momentum (kgm/sec or lbft/sec), m = mass (kg or lb), and v = velocity (m/s or ft/sec).
What is Momentum Formula?
This equation corresponds neatly with the earlier definition of momentum as "mass in motion." When the motion is rotational, however, the mass's distance from the rotational axis comes into play.
As a result, angular momentum is calculated as the product of rotational inertia and angular velocity: L = I,
where,
- L denotes angular momentum (kg•m2/sec or lb•ft2/sec)
- I denotes a rotating moment of inertia (kg•m2 or lb•ft2)
- rad denotes angular velocity (rad/sec).
Inertia is an important factor in motor sizing calculations for motion applications.
- If the inertia of the motor is significantly less than that of the load or system, the motor will have difficulty driving and controlling the load, and response time and resonance will be high.
- If the motor inertia is much higher than the load or system inertia, the motor is probably excessive, and the system will be inefficient.
- Although momentum is not directly considered when sizing motion components, its impact is noticeable.
- Returning to the ice skater example, the principle of conservation of angular momentum dictates that the skater's speed must increase when her arms are drawn in close to her body.
- Her angular velocity must increase when her inertia is reduced (I = mr2 where r is reduced) in order for her angular momentum to remain constant.
Also Read: Mass and Momentum
Types of Momentum
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The different types of momentum are:
Angular Momentum
Angular momentum is a physical quantity which is a measure of the amount of rotational motion of a rotating object.
- It is a vector quantity, which means that it is both magnitude and direction.
- The magnitude of the angular momentum is proportional to the product of the moment of inertia and the angular velocity of the object, with the direction perpendicular to the plane of rotation.
- The formula for angular momentum is L = Iω, where L is angular momentum, I is the moment of inertia, and ω is angular velocity.
- Angular momentum is conserved in the absence of external torques, meaning that the total angular momentum of a system remains constant.
Angular Momentum
Linear Momentum
The quantity of mass associated with a body moving along a straight route is known as linear momentum, sometimes known as force.
- Linear momentum is a physical quantity which is a measure of the amount of motion of a moving object.
- It is a vector quantity.
- Linear Momentum is also often referred to as translational momentum.
- The magnitude of the linear momentum of an object is equal to the product of its mass and velocity, while the direction is the same as the direction of its velocity.
Check More: Difference Between Force and Momentum
Difference Between Inertia and Momentum
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The differences between inertia and momentum are tabulated below:
| Momentum | Inertia |
|---|---|
| Momentum is a measure of the motion of an object and is the product of its mass and velocity. | Inertia is the property of matter that resists any change in its state of motion, either rest or uniform motion in a straight line. |
| Momentum is represented as “p”. | Inertia can be represented as “I” |
| Momentum can be divided into two types, Linear and Angular Momentum. | There are three types of inertia, namely, the inertia of rest, the inertia of motion, and the inertia of direction. |
| The momentum of a body of mass ‘m’ moving with a velocity of ‘v’ can be calculated with the formula, p = m × v. | Inertia cannot be evaluated by using any formula. |
| Momentum is a vector quantity. | Inertia is a scalar quantity. |
| Momentum is dependent upon Mass and Velocity. | Inertia, however, depends on mass. |
| The total momentum is conserved in case of Momentum. | Inertia has nothing to do with the conservation of energy. |
Momentum is a property of a moving item, while inertia is a concept that helps us better grasp and explain mechanics. The main distinction between momentum and inertia is that momentum can be calculated physically, whereas inertia cannot.
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Things to Remember
- Momentum is inertia in motion and is defined as an object’s mass time velocity
- Inertia is the resistance of a body to change its speed, and it is proportional to its mass and distance from the axis of rotation.
- Inertia has nothing to do with the conservation of energy.
- There are three types of inertia: Inertia of rest, Inertia of motion and Inertia of direction.
- Momentum is a vector quantity while Inertia is a scalar quantity.
- Momentum can be calculated physically while Inertia cannot be calculated with a formula.
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Sample Questions
Ques. What causes inertia? (3 marks)
Ans. Because inertia is defined as "the tendency for a motion to remain unchanging," it simply refers to the measurement of an object's ability to maintain a constant velocity, direction, speed, or position.
According to Newton's first law, "If the resultant force of a stationary object is 0 N, the object will remain stationary. If the resulting force on a moving object is 0 N, the object will keep moving at the same speed "' (Velocity is a vector with speed and direction, thus it has the same speed and direction.).
As a result, resistance is the source of inertia, because inertia is the resistance of any moving or stationary object to change its state of motion, or, as previously said, "the tendency for a motion to remain unchanging." Changes in force According to Newton's first law, if the resultant force is 0 N, a stationary item will remain motionless and a moving object will continue to move at the same velocity, but resistance is what causes it.
Ques. How do you explain inertia? (2 marks)
Ans. The resistance of any physical object to any change in velocity is known as inertia. The tendency of objects to continue travelling in a straight line at a steady speed when no forces occur on them is one example of this feature. There are three types of inertia:
- Inertia of Rest
- Inertia of Motion
- Inertia of Direction
Ques. What is the moment of inertia for a hollow cylinder? (3 marks)
Ans. The moment of inertia for the hollow cylinder is given by:
- Moment of inertia about the x-axis of a mass: Ix= (m/12) * (3*(R22+R12) + h2)
- Moment of inertia about the y axis of mass: Iy= (m/12) * (3*(R22+R12) + h2)
- Moment of inertia about the z-axis of mass: Iz= (m/2) * (R12+R22)
Ques. How is a moment of inertia measured? (2 marks)
Ans. The moment of inertia unit is a composite measurement unit. m is measured in kilograms and r is measured in metres in the International System (SI), with I (moment of inertia) having a kilogram-meter square area.
Moments of inertia is found by integrating every ‘piece of mass’ that makes up an object, multiplied by the square of the distance of each ‘piece of mass’ to the axis.
Ques. How is momentum measured? (2 marks)
Ans. The mass of an object multiplied by the velocity of the object equals the object's momentum. The momentum will be measured in kilogram metres per second (kg m/s) since the mass will be measured in kilogrammes (kg) and the velocity in meters per second (m/s).
Momentum is the product of the mass of the object and the velocity of the object.
Ques. How are momentum and inertia related? (2 marks)
Ans. Momentum is a measurement of how much motion is present in a moving item, and it is determined by the mass and velocity of the object. The only items that can have momentum are those that are moving. The resistance of an object to change its state of motion is referred to as inertia.
Inertia is the barrier to the motion of an object, whereas momentum is the tendency of a thing to continue moving. While inertia is a critical sizing characteristic, momentum isn't directly handled in system calculations.
Ques. How do you find a moment of inertia of a sphere? (3 marks)
Ans. Summing the moments of infinitesimally thin discs around the z-axis can be used to derive the expression for a sphere's moment of inertia.
Ques. What is the law of conservation of momentum example? (2 marks)
Ans. For a collision between two bodies, the law of conservation of momentum applies. Total momentum before and after the impact is equal to the total momentum after the collision. m1u1 + m2u2 = m1v1 + m2v2.
For instance, when a gun fires a shot, the gun recoils. When you fire a shot, it leaves the barrel with a particular amount of force.
Ques. A 60 g bullet which is fired from a 5 kg gun is seen to leave with a speed of 500 m/s. Determine the speed or velocity with which the gun recoils back, which means it jerks back. (3 marks)
Ans. As per the given data,
Mass of Bullet, m1 = 60 g = 0.06 kg
Velocity of Bullet v1 = 500 m/s
Mass of Gun m2 = 5 kg
As per the Law of Conservation of Momentum
m1 x v1 = m2 x v2
0.06 x 500 = 5 x v2
v2 = \(\frac{0.06 \times 500}{5}\) = 6 m/s
Ques. What is Angular Momentum? (2 marks)
Ans. Angular momentum is a concept in physics that describes the motion of rotating objects. It is a measure of the amount of rotational motion an object has, and is defined as the product of the moment of inertia of the object and its angular velocity.
Simply, the angular momentum of a rotating object is the vector cross product of the object's position vector and its linear momentum vector. In equation form, it is expressed as:
L = Iω
where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity of the object.
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