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Laws of Motion - The Law of Inertia

Grade 11CBSEPhysics

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Newton's First Law of Motion: An object continues to be in its state of rest or of uniform motion in a straight line unless compelled by some external force to act otherwise.

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Definition of Inertia: Inertia is the inherent property of a body by virtue of which it resists any change in its state of rest or uniform motion in a straight line.

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Mass as a Measure of Inertia: The inertia of an object is measured by its mass. A heavier object (more mass) has more inertia than a lighter object, meaning it requires more force to change its state of motion.

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Inertia of Rest: The inability of a body to change by itself its state of rest. Example: When a bus starts suddenly, the passengers fall backwards because their lower body moves with the bus while the upper body tends to remain at rest.

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Inertia of Motion: The inability of a body to change by itself its state of uniform motion. Example: A passenger jumps out of a moving train and falls forward because his feet touch the ground and stop, but his upper body continues to move forward.

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Inertia of Direction: The inability of a body to change by itself its direction of motion. Example: When a car takes a sharp turn, the passengers are thrown outwards because their bodies tend to continue moving in the original straight line.

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Inertial Frame of Reference: A coordinate system in which Newton's first law holds true. Non-accelerating frames (either at rest or moving with constant velocity) are considered inertial frames.

📐Formulae

If ∑F⃗ext=0, then v⃗=constant\text{If } \sum \vec{F}_{ext} = 0, \text{ then } \vec{v} = \text{constant}

a⃗=dv⃗dt=0  ⟺  ∑F⃗ext=0\vec{a} = \frac{d\vec{v}}{dt} = 0 \iff \sum \vec{F}_{ext} = 0

Inertia∝Mass (m)\text{Inertia} \propto \text{Mass (m)}

💡Examples

Problem 1:

A book of mass m=2 kgm = 2\text{ kg} is lying on a horizontal table. If the net external force acting on the book is zero, what is its acceleration?

Solution:

a⃗=0 m/s2\vec{a} = 0\text{ m/s}^2

Explanation:

According to the Law of Inertia (Newton's First Law), if the net external force ∑F⃗ext\sum \vec{F}_{ext} acting on an object is zero, the object will maintain its state of rest. Since the book is initially at rest and the net force is zero, its acceleration must be zero.

Problem 2:

Consider a spaceship moving in deep space, far from any gravitational influence, with a constant velocity of 1000 m/s1000\text{ m/s}. How much force is required to keep it moving at this velocity?

Solution:

F=0 NF = 0\text{ N}

Explanation:

According to the Law of Inertia, an object in uniform motion will continue to move with the same constant velocity unless acted upon by an external force. In the absence of friction and gravity, no force is required to maintain a constant velocity.

Problem 3:

Calculate the total mass of a system if three objects with masses m1=15 kgm_1 = 15\text{ kg}, m2=25 kgm_2 = 25\text{ kg}, and m3=10 kgm_3 = 10\text{ kg} are placed together. Show the vertical addition.

Solution:

1525+1050\begin{array}{r} 15 \\ 25 \\ + 10 \\ \hline 50 \end{array} Total Mass = 50 kg50\text{ kg}

Explanation:

Inertia is additive because mass is a scalar quantity. The total inertia of the system is represented by the sum of the individual masses.