Newton's Second Law of Motion
All the forces acting on a body form the net force.
Net force on a body causes it to accelerate.
Acceleration is directly proportional to the net force.
If you double the net force on a body, the acceleration doubles; if you triple the net force, the acceleration triples, and so on.
Acceleration ~ Net force
‘~’ means ‘directly proportional to’.
Friction acts between two surfaces when:
They slide over one another, or,
They have a tendency to slide over one another. (They’re not actually sliding, but they have the intention to).
Friction is an obstructive force.
It reduces the net force and acceleration.
It occurs due to irregularities on a surface.
Even a surface that seems smooth has microscopic irregularities on it. An object sliding over it has to either rise over the bumps or scrape the atoms off.
Direction of friction is always opposite to the direction of motion.
A moving object has friction acting against it. For the object to keep moving at a constant velocity, a force equal and opposite to the force of friction needs to be applied on it.
How friction builds:
Consider a crate at rest on the floor. It isn’t moving.
There is just enough friction holding it in place.
If you push it with a force of say 70N, the friction builds up to 70N, and the crate still doesn’t move.
If you push it with a force of 100N, the friction builds again, but the crate is on the verge of sliding.
If you push with a larger force, the friction won’t be able to hold the crate in place anymore, and the crate will start moving.
Types of friction:
Static friction → friction that builds up just before the object starts moving
Sliding friction → friction acting on the object once it actually starts moving
Static friction > Sliding friction
Consider a car. When the car is rolled smoothly to a stop, static friction holds the wheels in place.
When you slam the breaks, the tires lock and slide, causing sliding friction, which is considerably lesser than static friction. It’s harder for the car to not move.
This is why we have antilock brake systems.
Friction doesn’t depend on speed.
Two cars skidding at different speeds would have roughly the same friction acting on their tires.
Friction doesn’t depend on the area of contact.
The friction between a wider tire and a narrower tire would be the same.
The friction between a truck and the ground would be the same whether the truck has four wheels or eighteen.
Fluid Friction:
Friction that occurs in fluids (liquids or gases).
It happens when an object pushes aside the fluid it is moving through.
It depends on speed.
Air resistance (or air drag) is a type of fluid friction.
MASS | WEIGHT |
|---|---|
→ the quantity of matter in an object. | → usually the force due to gravity acting on an object. |
→ Mass is a measure of the inertia an object exhibits in response to any effort made to change its state of motion. | → An object can have weight without the force of gravity. Eg: in a rotating space station |
Weight of an object, w = mg
m = mass
g = acceleration due to gravity
Mass is directly proportional to weight.
Weight corresponds to our notion of inertia. For instance, shaking two objects to see which is heavier/more difficult to move. You’re actually comparing inertias of the objects.
In the US, the amount of matter is measured in pounds (lbs). In the rest of the world, it’s measured in kgs.
The unit of force is newton.
1kg = 10N (more precisely, 9.8N)
Away from the Earth’s surface, the force of gravity is either lesser or more.
1kg on Earth = 0.36lbs on the Moon
Stronger force of gravity → more weight.
Weaker force of gravity → less weight.
The mass of an object stays the same everywhere.
An object offers the same resistance to speeding up or slowing down wherever it is.
The size of an object (volume) is not a good indicator of its mass.
It’s easier to move an empty cardboard box than a car’s battery of the same size.
It’d be harder to push an elephant on a skateboard than a person on a skateboard.
The same force applied to:
twice the mass, would produce half the acceleration
one-third of the mass, would produce three times the acceleration
Acceleration ~ 1/mass
Acceleration is inversely proportional to mass.
inversely → in a relationship between two values, if one doubles, the other halves.
Statement:
The acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object.
What it means:
Acceleration of an object:
increases with an increase in the net force applied to the object, and vice versa.
decreases with an increase in the mass of the object, and vice versa.
is in the direction of the net force being applied.
Acceleration ~ net force/mass
Summarized form of Newton’s second law.
‘~’ → is proportional to
Acceleration = Net Force/Mass
If a force is being applied:
in the direction of motion of the object, the object accelerates.
opposite to the direction of motion of the object, the object decelerates (slows down).
at right angles to the direction of motion of the object, the object deflects.
An object falling towards the Earth accelerates due to gravity.
When there’s no resistance to the fall (such as friction, air resistance), the object is in a state of free fall.
Greater the mass of the object, greater the gravitational force of attraction between it and the Earth.
An object two times heavier than another doesn’t fall twice as fast.
This is because the acceleration of the fall depends on inertia of the object, too.
Inertia → resistance to the acceleration produced by a force
g → acceleration due to gravity
Ratio of gravitational force to mass for a freely falling object is a constant, g.
Acceleration due to free fall doesn’t depend on the mass of the object.
Consider a pebble and a boulder with a mass 100 times that of the pebble.
Both fall with the same acceleration.
Reason: The gravitational pull on the boulder is 100x more, but the boulder’s resistance to change in motion is also 100x more than the pebble’s.
Newton’s laws apply for all objects.
A feather and a coin would fall equally fast in a vacuum, but differently in air.
In a vacuum, the net force acting on a falling object is only due to gravity.
In air, the net force is lesser than the force due to gravity, because of the opposing air resistance.
Force of air resistance a falling object experiences depends on:
Size (how big the frontal area of the object is)
Speed (proportional to the number of air molecules encountered per second)
mg → force due to gravity
R → air resistance
m → mass
Considering a diagram: 
Air resistance/drag would have a greater impact on a lighter object than on a heavier object.
Air drag opposes a falling object. When the acceleration of the object becomes zero, it has reached terminal speed.
When considering direction, for a falling object, we say it has reached its terminal velocity.
Another example:
→ Consider a skydiver falling.
→ The speed increases until the air resistance finally equals the gravitational force acting on the diver.
→ At this point, they no longer accelerate. Terminal velocity is reached.
Note: Skydivers fall head/feet first to minimize air drag and maximize terminal velocity.
A skydiver’s terminal velocity is decreased by spreading out, or by wearing a wingsuit.
Wingsuits increase the frontal area.
Parachutes provide large frontal areas to reduce terminal speed.
→ Consider a man and a woman using parachutes of the same size.
→ If they were falling at the same speed, the air resistance acting on either of them would be the same, and they’d hit the ground at the same time.
→ If they were falling at different speeds, the person with the higher terminal speed would hit the ground first.
→ Considering the man to be heavier, it would take a larger amount of air resistance to match the force of gravity pulling him downwards, than it would the woman (the lighter of the two).
→ So, he’d fall faster, and hit the ground first.
The heavier the object, the greater the terminal velocity.
Another example:
Consider two tennis balls. One is hollow. The other is filled with iron pellets.
Case 1: Both balls are dropped from above your head.
Case 2: Both balls are dropped from the top of a building.
Case 1, Observation:
Both balls would hit the ground at nearly the same time.
Reason → The air resistance compared to the force of gravity acting on the balls is minimal.
The difference in the landing timings of the balls is negligible.
Case 2, Observation:
The ball with the iron pellets is noticeably heavier. It would hit the ground first.
Reason → Since the balls are falling at a higher speed, there’s a greater air resistance acting on them.
Since both the balls are the same size, at any given speed, they’re experiencing the same air resistance.
But, because there’s a greater force of gravity acting on the heavier ball, air drag/resistance doesn’t decrease the net force acting on the ball as much as it does with the hollow (lighter) ball.
The net force acting on any falling object becomes zero when the air resistance becomes equal to the gravitational force acting on the object.
At this point, the acceleration terminates.
All the forces acting on a body form the net force.
Net force on a body causes it to accelerate.
Acceleration is directly proportional to the net force.
If you double the net force on a body, the acceleration doubles; if you triple the net force, the acceleration triples, and so on.
Acceleration ~ Net force
‘~’ means ‘directly proportional to’.
Friction acts between two surfaces when:
They slide over one another, or,
They have a tendency to slide over one another. (They’re not actually sliding, but they have the intention to).
Friction is an obstructive force.
It reduces the net force and acceleration.
It occurs due to irregularities on a surface.
Even a surface that seems smooth has microscopic irregularities on it. An object sliding over it has to either rise over the bumps or scrape the atoms off.
Direction of friction is always opposite to the direction of motion.
A moving object has friction acting against it. For the object to keep moving at a constant velocity, a force equal and opposite to the force of friction needs to be applied on it.
How friction builds:
Consider a crate at rest on the floor. It isn’t moving.
There is just enough friction holding it in place.
If you push it with a force of say 70N, the friction builds up to 70N, and the crate still doesn’t move.
If you push it with a force of 100N, the friction builds again, but the crate is on the verge of sliding.
If you push with a larger force, the friction won’t be able to hold the crate in place anymore, and the crate will start moving.
Types of friction:
Static friction → friction that builds up just before the object starts moving
Sliding friction → friction acting on the object once it actually starts moving
Static friction > Sliding friction
Consider a car. When the car is rolled smoothly to a stop, static friction holds the wheels in place.
When you slam the breaks, the tires lock and slide, causing sliding friction, which is considerably lesser than static friction. It’s harder for the car to not move.
This is why we have antilock brake systems.
Friction doesn’t depend on speed.
Two cars skidding at different speeds would have roughly the same friction acting on their tires.
Friction doesn’t depend on the area of contact.
The friction between a wider tire and a narrower tire would be the same.
The friction between a truck and the ground would be the same whether the truck has four wheels or eighteen.
Fluid Friction:
Friction that occurs in fluids (liquids or gases).
It happens when an object pushes aside the fluid it is moving through.
It depends on speed.
Air resistance (or air drag) is a type of fluid friction.
MASS | WEIGHT |
|---|---|
→ the quantity of matter in an object. | → usually the force due to gravity acting on an object. |
→ Mass is a measure of the inertia an object exhibits in response to any effort made to change its state of motion. | → An object can have weight without the force of gravity. Eg: in a rotating space station |
Weight of an object, w = mg
m = mass
g = acceleration due to gravity
Mass is directly proportional to weight.
Weight corresponds to our notion of inertia. For instance, shaking two objects to see which is heavier/more difficult to move. You’re actually comparing inertias of the objects.
In the US, the amount of matter is measured in pounds (lbs). In the rest of the world, it’s measured in kgs.
The unit of force is newton.
1kg = 10N (more precisely, 9.8N)
Away from the Earth’s surface, the force of gravity is either lesser or more.
1kg on Earth = 0.36lbs on the Moon
Stronger force of gravity → more weight.
Weaker force of gravity → less weight.
The mass of an object stays the same everywhere.
An object offers the same resistance to speeding up or slowing down wherever it is.
The size of an object (volume) is not a good indicator of its mass.
It’s easier to move an empty cardboard box than a car’s battery of the same size.
It’d be harder to push an elephant on a skateboard than a person on a skateboard.
The same force applied to:
twice the mass, would produce half the acceleration
one-third of the mass, would produce three times the acceleration
Acceleration ~ 1/mass
Acceleration is inversely proportional to mass.
inversely → in a relationship between two values, if one doubles, the other halves.
Statement:
The acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object.
What it means:
Acceleration of an object:
increases with an increase in the net force applied to the object, and vice versa.
decreases with an increase in the mass of the object, and vice versa.
is in the direction of the net force being applied.
Acceleration ~ net force/mass
Summarized form of Newton’s second law.
‘~’ → is proportional to
Acceleration = Net Force/Mass
If a force is being applied:
in the direction of motion of the object, the object accelerates.
opposite to the direction of motion of the object, the object decelerates (slows down).
at right angles to the direction of motion of the object, the object deflects.
An object falling towards the Earth accelerates due to gravity.
When there’s no resistance to the fall (such as friction, air resistance), the object is in a state of free fall.
Greater the mass of the object, greater the gravitational force of attraction between it and the Earth.
An object two times heavier than another doesn’t fall twice as fast.
This is because the acceleration of the fall depends on inertia of the object, too.
Inertia → resistance to the acceleration produced by a force
g → acceleration due to gravity
Ratio of gravitational force to mass for a freely falling object is a constant, g.
Acceleration due to free fall doesn’t depend on the mass of the object.
Consider a pebble and a boulder with a mass 100 times that of the pebble.
Both fall with the same acceleration.
Reason: The gravitational pull on the boulder is 100x more, but the boulder’s resistance to change in motion is also 100x more than the pebble’s.
Newton’s laws apply for all objects.
A feather and a coin would fall equally fast in a vacuum, but differently in air.
In a vacuum, the net force acting on a falling object is only due to gravity.
In air, the net force is lesser than the force due to gravity, because of the opposing air resistance.
Force of air resistance a falling object experiences depends on:
Size (how big the frontal area of the object is)
Speed (proportional to the number of air molecules encountered per second)
mg → force due to gravity
R → air resistance
m → mass
Considering a diagram:
Air resistance/drag would have a greater impact on a lighter object than on a heavier object.
Air drag opposes a falling object. When the acceleration of the object becomes zero, it has reached terminal speed.
When considering direction, for a falling object, we say it has reached its terminal velocity.
Another example:
→ Consider a skydiver falling.
→ The speed increases until the air resistance finally equals the gravitational force acting on the diver.
→ At this point, they no longer accelerate. Terminal velocity is reached.
Note: Skydivers fall head/feet first to minimize air drag and maximize terminal velocity.
A skydiver’s terminal velocity is decreased by spreading out, or by wearing a wingsuit.
Wingsuits increase the frontal area.
Parachutes provide large frontal areas to reduce terminal speed.
→ Consider a man and a woman using parachutes of the same size.
→ If they were falling at the same speed, the air resistance acting on either of them would be the same, and they’d hit the ground at the same time.
→ If they were falling at different speeds, the person with the higher terminal speed would hit the ground first.
→ Considering the man to be heavier, it would take a larger amount of air resistance to match the force of gravity pulling him downwards, than it would the woman (the lighter of the two).
→ So, he’d fall faster, and hit the ground first.
The heavier the object, the greater the terminal velocity.
Another example:
Consider two tennis balls. One is hollow. The other is filled with iron pellets.
Case 1: Both balls are dropped from above your head.
Case 2: Both balls are dropped from the top of a building.
Case 1, Observation:
Both balls would hit the ground at nearly the same time.
Reason → The air resistance compared to the force of gravity acting on the balls is minimal.
The difference in the landing timings of the balls is negligible.
Case 2, Observation:
The ball with the iron pellets is noticeably heavier. It would hit the ground first.
Reason → Since the balls are falling at a higher speed, there’s a greater air resistance acting on them.
Since both the balls are the same size, at any given speed, they’re experiencing the same air resistance.
But, because there’s a greater force of gravity acting on the heavier ball, air drag/resistance doesn’t decrease the net force acting on the ball as much as it does with the hollow (lighter) ball.
The net force acting on any falling object becomes zero when the air resistance becomes equal to the gravitational force acting on the object.
At this point, the acceleration terminates.
