Laws of Motion – Explanation in Detail
Isaac Newton discovered the Laws of Motion. Newton’s laws of motion explain the connection between a physical object and the forces acting upon it. By understanding the concept, it provides all the information about the basis of modern physics. After the development of the three laws of motion, Newton revolutionized science. Newton’s three laws together with Kepler’s Laws explained the concept of planets moving in elliptical orbits rather than in circles. Although Newton’s laws of motion may seem so general today, they were considered revolutionary centuries ago. Newton’s three laws of motion help someone understand how objects behave when standing still, when moving and when forces act upon them. Sir Newton’s three laws are Newton’s First Law: Inertia, Newton’s Second Law: Force, Newton’s Third Law: Action & Reaction.
Newton’s First Law
Newton’s First Law states that ‘An object at rest remains at rest, and an object in motion remains in motion at a constant speed and in a straight line unless acted on by an unbalanced force’. This law describes that every object will remain at rest or in uniform motion in a straight line unless forced to change its state by the action of an external force. The tendency of an object to resist changes in a state of motion is inertia. There will be a net force on an object if all the external forces cancel each other out. If this happens, then the object will maintain a constant velocity. If the Velocity remains at zero, then the object remains at rest. If any external force acts on an object, the velocity will change because of the force applied. An example of the First law of motion is : The motion of a round ball falling down through the atmosphere, A rocket being launched up into the atmosphere.
Newton’s Second Law
Newton’s Second Law states that ‘The acceleration of an object depends on the mass of the object and the amount of force applied’. This law defines a force to be equal to a change in momentum (mass times velocity) per change in time. Momentum is described as the mass m of an object times its velocity V. Example of the second law of motion is: An aircraft’s motion resulting from the aerodynamic force, aircraft thrust and weight.
Newton’s Third Law
Newton’s Third Law states that ‘Whenever one object implies a force on a second object, the second object implies an equal and opposite force on the first’. This law defines that for every action in nature there is an equal and opposite reaction. If object A applied a force on object B, object B will also apply an equal and opposite force on object A. In other words, it can be said that forces result from interactions. An example of the third law of motion is: The motion of a jet engine produces thrust and hot exhaust gasses flow out the back of the engine, and a thrusting force is produced in the opposite direction.
Derivation of First Equation of Motion
Let’s Consider a body of mass m having initial velocity u.
Let after time be t its final velocity becomes v due to uniform acceleration a.
Now it is defined as:
Acceleration = Change in velocity / Time taken
Acceleration = (Final velocity - Initial velocity) / Time taken
a = (v - u) / t
a t = v - u
or v = u + at
This describes the first equation of motion.
Derivation of Second Equation of Motion
As it is defined, the Second equation of motion: s = ut + (1/2) at2
Let’s take the distance traveled by the body be s.
Now:
Distance = Average velocity x Time
Also, Average velocity = (u + v) / 2
Therefore, Distance (t) = (u + v) / 2t ......eq.(1)
Again from first equation of motion:
v = u + at
Substituting this value of v in eq.(1), we get
s = (u + u + at) / 2t
s = (2u + at) / 2t
s = (2ut + at2) / 2
s = (2ut / 2) + (at2 / 2)
or s = ut + (1/2) at2
This describes the second equation of motion.
Derivation of Third Equation of Motion
As it is defined that the third equation of Motion: v2 = u2 + 2as
Now,
v = u + at
v - u = at
or t = (v - u) / a ........ eq.(2)
Also ,
Distance = average velocity x Time
Therefore, s = ((v + u) / 2) x ((v - u) / a)
s = (v2 - u2) / 2a
2as = v2 - u2
or v2 = u2 + 2as
This describes the third equation of motion.
FAQs on Laws of Motion
1. What are Newton's three laws of motion?
Newton's three laws of motion describe the relationship between an object and the forces acting upon it. They form the foundation of classical mechanics. The three laws are:
- First Law (Law of Inertia): An object remains at rest or in uniform motion in a straight line unless acted upon by an external unbalanced force.
- Second Law (Law of Acceleration): The rate of change of momentum of an object is directly proportional to the applied external force, and this change takes place in the direction of the force. Mathematically, F = dp/dt, which simplifies to F = ma when mass is constant.
- Third Law (Law of Action and Reaction): For every action, there is an equal and opposite reaction. These forces act on two different bodies.
2. What is inertia and how does it relate to Newton's First Law of Motion?
Inertia is the inherent property of a physical object to resist any change in its state of rest or of uniform motion. Newton's First Law is often called the Law of Inertia because it directly defines this concept. The law states that an object will not change its velocity (either from zero or a constant value) unless an external force compels it to. Essentially, the more mass an object has, the greater its inertia, and the harder it is to change its state of motion.
3. What is the difference between the two common formulas for Newton's Second Law, F = ma and F = dp/dt?
Both formulas represent Newton's Second Law, but they have different scopes of application:
- F = ma (Force = mass × acceleration) is a special case of the second law. It is only applicable when the mass (m) of the system remains constant. It is widely used in problems involving everyday objects with fixed mass.
- F = dp/dt (Force = rate of change of momentum) is the more general and fundamental form of the law. It is always true, even for systems where the mass changes, such as a rocket ejecting fuel or a conveyor belt dropping sand. Since momentum (p) is the product of mass and velocity (p = mv), this form accounts for changes in both mass and velocity.
4. Why don't the action-reaction forces in Newton's Third Law cancel each other out?
This is a common point of confusion. The action and reaction forces described in Newton's Third Law do not cancel each other out because they act on different objects. For forces to cancel, they must act on the same object. For example, when you push a wall (action), the wall pushes back on you (reaction). The force you exert acts on the wall, and the force the wall exerts acts on you. Since the forces are on separate bodies, they cannot be added together to yield a net force of zero on a single body.
5. What is the relationship between impulse and momentum?
Impulse is directly related to the change in momentum. According to Newton's Second Law, Force (F) is the rate of change of momentum (p). The Impulse-Momentum Theorem states that the impulse applied to an object is equal to the change in its momentum. Impulse is defined as the product of the force and the time interval over which it acts (Impulse = F × Δt). Therefore, the relationship is: F × Δt = Δp, where Δp is the change in momentum. This shows that a large force applied for a short time can produce the same change in momentum as a small force applied for a longer time.
6. What is the difference between static friction and kinetic friction?
Static and kinetic friction are two types of frictional forces that oppose motion or the tendency of motion between surfaces in contact.
- Static Friction (fₛ): This is the force that prevents an object from starting to move. It is a self-adjusting force that increases as the applied force increases, up to a maximum limit called the limiting friction. It acts when the object is at rest.
- Kinetic Friction (fₖ): This is the force that opposes the motion of an object that is already moving. It is generally less than the maximum static friction and remains relatively constant as long as the object is in motion. This is why it's often harder to start pushing a heavy box than to keep it moving.
7. How does the law of conservation of linear momentum explain the recoil of a gun?
The law of conservation of linear momentum states that if no external force acts on a system, its total momentum remains constant. A gun and a bullet can be considered an isolated system. Before firing, both are at rest, so the total initial momentum is zero. When the gun is fired, the bullet moves forward with a certain momentum. To keep the total momentum of the system zero, the gun must move backward with an equal and opposite momentum. This backward motion of the gun is known as recoil.
8. What is centripetal force and what provides it for a car turning on a level road?
Centripetal force is not a new type of force; it is the net force required to keep an object moving in a circular path. This force is always directed towards the centre of the circle. For a car making a turn on a level (unbanked) road, the centripetal force is provided entirely by the force of static friction between the car's tires and the road surface. If the frictional force is insufficient (e.g., on an icy or wet road), the car will not be able to make the turn and will skid outwards.
