Newton’s First Law Of Motion

Newton's First Law Of Motion

Newton’s 1st law of motion states that if the (vector) sum of all the forces acting on a particle is zero, then and only then does the particle remain unaccelerated, i.e., remains at rest or move with constant velocity.

If $\mathrm{F}_{\text {net }}=0 \Rightarrow \mathrm{a}_{\text {net }}=0 \Rightarrow$ forces in all directions are zero,i.e,

$\sum \vec{F}_x=0, \sum \vec{F}_y=0, \sum \vec{F}_z=0$

Newton’s first law is also called the law of inertia.

Newton’s laws are valid in an inertial frame of reference but are not valid in a non-inertial frame of reference. Frame of reference

A frame of reference is a system of coordinate systems and clocks.

Types of frame of reference:

There are mainly two types of frame of reference one is internal frame of rfrefrance and another is a non internal frame of reference.

• Inertial frame of reference- A frame which is at rest or moving with uniform velocity.

Example- 1. Car moving with velocity v on a straight road, Lift at rest.

• A non-inertial frame of reference- A frame which is accelerated and does not have a constant velocity.

Example- 1. The frame travels in a straight line but speeding up or slowing down.

2. The frame travels along a curved path.

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Solved Example Based on Newton's First Law Of Motion

Example 1: Choose the correct option.

In which Kind of motion an object in motion will stay in motion as long as the net forces acting on it are zero?

1) Slowing motion in a straight line

2) Accelerating motion in a straight line

3) Constant motion in a straight line

4) All of these

Solution:

As we learned

Newton’s 1st law of motion states that if the vector sum of all the forces acting on a particle is zero, then and only then does the particle remain unaccelerated, i.e., remains at rest or moves with constant velocity.

So for a Constant motion in a straight line if the net forces acting on it are zero then the object in motion will stay in motion.

Hence, the answer is the option (3).

Example 2:|Two blocks of masses $m_1=5 / \sqrt{3} \mathrm{~kg}_{\text {and }} m_2=5 \mathrm{~kg}$ are released from rest on a frictionless inclined plane as shown in fig then-

1) The block A moves down the plane

2) Block B moves down the plane

3) Both blocks remain at rest.

4) Both blocks move down the plane.

Solution

$\text { Free body diagram of given system : }$

$\text { Component of weight responsible for downward movement of the blocks is } m g \sin \theta$

For block A :mg $\sin \theta=m g \sin 60^{\circ}=\frac{5}{\sqrt{3}} \times \frac{\sqrt{3}}{2}=2.5 N$ For block B : $m g \sin \theta=m g \sin 30^{\circ}=5 \times \frac{1}{2}=2.5 \mathrm{~N}$ Since, $m g \sin 60^{\circ}=m g \sin 30^{\circ}$ is same.

Hence Both blocks remain at rest.

Example3 :A block is kept on a frictionless inclined surface with an angle of inclination $\alpha$. The incline is given an acceleration to keep the block stationary. then a is equal to

1) $g$
2) $g \tan \alpha$
3) $g / \tan \alpha$
4) $g \operatorname{cosec} \alpha$

Solution :

$\text { Free body diagram of wedge : }$

For block to remain stationary,

$m a \cos \alpha=m g \sin \alpha$
$
\therefore a=g \tan \alpha
$

Hence, the answer is option (2).

Example 4: While pushing a very heavy box, Derek noticed that it was harder for him to get the box to start moving. This is an example of which mechanics principle?

1) Newton’s first law

2) Law of universal gravitation

3) Newton’s second law

4) Newton’s third law

Solution:

This is an example of Newton's first law: An object at rest will remain at rest, and an object in motion will remain in motion in that direction unless acted upon by an outside force.

Inertia is effectively nature’s way of trying to avoid change. This explains why the box is hard to move while it is still; it requires a change to get it to move from rest to moving.

When we try to push a very heavy box kept on the ground, it does not move at all because the weight of the box and frictional force acting due to roughness between the contact surfaces prevent this box from moving forward.

Hence, the answer is option (1).

Example 5: A boy pushes a box of mass $2 \mathrm{~kg}$ with a force $\vec{F}=(20 \hat{i}+10 \hat{j}) N$ on a frictionless surface. If the box was initially at rest, then $\qquad$ $\mathrm{m}$ is displacement along the $\mathrm{x}$-axis after $10 \mathrm{~s}$.

1) 500

2) 100

3) 200

4) 600

Solution

$
\begin{array}{ll}
\vec{F}=(20 \hat{i}+10 \hat{j}) N & S_x=u_x t+\frac{1}{2} a_x t^2 \\
F_x=20 N & \text { Displacement along } x \text {-axis is } S_x=0 \times 10+\frac{1}{2} \times 10 \times(10)^2 \\
F_y=10 \mathrm{~N} & =500 \mathrm{~m} \\
a_x=\frac{F_x}{M}=\frac{20}{2}=10 \mathrm{~m} / \mathrm{s}^2 \quad
\end{array}
$

Displacement along $x$-axis is $S_x=0 \times 10+\frac{1}{2} \times 10 \times(10)^2$

Hence, the answer is option (1).

Summary

Newton's First Law underlies all the basic mechanics of the way objects move and interact. It leads immediately to the conclusion that in the absence of forces due to factors like friction or air resistance, for instance, an object will continue on its course indefinitely. This can be observed in space, where no proposed rocket propulsion is adapted in spacecraft yet it covers vast distances.

Understanding Newton's First Law is important because it applies to real-world situations, from everyday kinds of things such as pushing a shopping cart, to huge engineering projects, and it leads us into Newton's other two laws of motion and classical mechanics as a whole. Since this law lets us know that unless a force from an outside device is applied, motion (or not) will continue, it explains the natural actions that objects take and forms a foundation for logical progressions and applications of all more advanced notions in physics.