DYNAMICS

Introduction

In physics, mechanics is the study of motion. Mechanics is divided into two parts: Kinematics (describing how things move, using velocity and acceleration) and Dynamics (studying why things move, by examining the forces that cause changes in motion).

Brief Overview

graph TD; Mechanics-->Kinematics; Mechanics-->Dynamics; Kinematics-->How[How things move]; Dynamics-->Why[Why things move - Forces];

1. Newton's Laws of Motion

Sir Isaac Newton formulated three fundamental laws that govern the motion of macroscopic objects.
* First Law (Law of Inertia): An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction, unless acted upon by an unbalanced external force. Inertia is an object's resistance to changes in its state of motion (more mass = more inertia).
* Second Law (Force and Acceleration): The acceleration of an object depends directly on the net force acting upon the object, and inversely upon the mass of the object.
* Formula: $F = m \times a$ (Force = mass $\times$ acceleration). The unit of Force is the Newton (N).
* Third Law (Action and Reaction): For every action, there is an equal and opposite reaction. If object A exerts a force on object B, object B exerts an exactly equal and opposite force on object A.

MCQs - Newton's Laws

Which of Newton's laws is also known as the Law of Inertia?
a) First Law
b) Second Law
c) Third Law
d) Law of Universal Gravitation
Answer: a
According to Newton's Second Law, if you apply the exact same force to a heavy truck and a small bicycle, which will have greater acceleration?
a) The heavy truck
b) The small bicycle
c) They will have the same acceleration
d) Neither will accelerate
Answer: b (Acceleration is inversely proportional to mass).
The standard unit of force in the metric system is the:
a) Joule
b) Watt
c) Newton
d) Pascal
Answer: c
A rocket taking off by pushing exhaust gases downward and being thrust upward is a perfect example of:
a) Newton's First Law
b) Newton's Second Law
c) Newton's Third Law
d) The Law of Conservation of Energy
Answer: c (Action and Reaction).
If an object has a mass of 10 kg and accelerates at $2 \text{ m/s}^2$, what is the net force acting on it?
a) 5 N
b) 12 N
c) 20 N
d) 100 N
Answer: c ($F = 10 \times 2 = 20$).
If the net force on an object is zero, which of the following must be true?
a) The object is at rest
b) The object is accelerating
c) The object's velocity is constant
d) The object has zero mass
Answer: c (Velocity is constant, which could mean zero or a non-zero steady speed).
Which law explains why you fall backward in a bus when it suddenly starts moving?
a) Newton's First Law
b) Newton's Second Law
c) Newton's Third Law
d) Law of Conservation of Energy
Answer: a (Due to inertia).
A force of 50 N is applied to a mass of 5 kg. What is the acceleration?
a) $10 \text{ m/s}^2$
b) $0.1 \text{ m/s}^2$
c) $250 \text{ m/s}^2$
d) $55 \text{ m/s}^2$
Answer: a ($a = F / m = 50 / 5 = 10$).
When a bird flies, it pushes the air downward, and the air pushes the bird upward. This is an example of:
a) Newton's First Law
b) Newton's Second Law
c) Newton's Third Law
d) Inertia
Answer: c
The property of matter that resists changes in motion is called:
a) Force
b) Acceleration
c) Inertia
d) Weight
Answer: c

2. Momentum and Impulse

Momentum ($p$): "Mass in motion." All moving objects have momentum. It is calculated by multiplying an object's mass by its velocity. ($p = m \times v$). A heavy truck moving slowly can have the same momentum as a tiny bullet moving very fast.
Conservation of Momentum: In a closed system with no external forces, the total momentum before a collision is equal to the total momentum after the collision.
Impulse: A change in momentum. It is calculated by multiplying the Force applied by the Time it is applied ($Impulse = F \times \Delta t$). This is why airbags in cars save lives: they increase the time of the collision, thereby drastically reducing the force felt by your body to achieve the same change in momentum.

MCQs - Momentum

Momentum is calculated by multiplying an object's mass by its:
a) Acceleration
b) Volume
c) Velocity
d) Weight
Answer: c
If a 1000 kg car is moving at 20 m/s, what is its momentum?
a) $50 \text{ kg}\cdot\text{m/s}$
b) $1020 \text{ kg}\cdot\text{m/s}$
c) $20,000 \text{ kg}\cdot\text{m/s}$
d) $400,000 \text{ kg}\cdot\text{m/s}$
Answer: c
The principle that total momentum remains constant in a closed system before and after a collision is called:
a) Conservation of Mass
b) Conservation of Momentum
c) Newton's First Law
d) The Impulse Theorem
Answer: b
Car crumple zones and airbags are designed to increase the __ of a collision, thereby reducing the force on the passengers.
a) Velocity
b) Mass
c) Momentum
d) Time
Answer: d
Which has more momentum: A 5000 kg truck parked on the street, or a 2 kg skateboard moving at 5 m/s?
a) The truck
b) The skateboard
c) They have the same momentum
d) Cannot be determined
Answer: b (The truck has 0 velocity, so 0 momentum).
Impulse is equivalent to the change in:
a) Kinetic energy
b) Force
c) Momentum
d) Acceleration
Answer: c
A 2 kg ball is moving at 3 m/s. What impulse is required to stop it?
a) 5 Ns
b) 6 Ns
c) 1.5 Ns
d) 0 Ns
Answer: b (Impulse = change in momentum = $2 \times 3 = 6$).
Two skaters standing still push against each other. The total momentum of the system after they push is:
a) Greater than zero
b) Less than zero
c) Zero
d) Dependent on their masses
Answer: c (Initial momentum is zero, so final momentum is zero).
If you double the velocity of an object, its momentum:
a) Remains the same
b) Doubles
c) Quadruples
d) Halves
Answer: b
The unit of impulse is:
a) Newton-second (N·s)
b) Newton per second (N/s)
c) Joule (J)
d) Watt (W)
Answer: a

Fun Facts about Dynamics!

The Apple Myth: Isaac Newton probably wasn't hit on the head by an apple. He did, however, observe an apple falling in an orchard, which led him to realize that the same force pulling the apple down (gravity) is the exact same force keeping the moon in orbit!
Recoil: When a gun is fired, the bullet goes forward (action), and the gun kicks backward into the shooter's shoulder (reaction). Because the gun has much more mass than the bullet, its backward acceleration (recoil) is much slower than the bullet's forward acceleration, perfectly obeying $F=ma$!
Constant Speed: If you are in a car driving perfectly smoothly in a straight line at 100 km/h, your body feels absolutely no net force. You only feel force when you accelerate, brake, or turn!