Classical Mechanics - Kinematics, Dynamics & Energy Flashcards

Question 1

Define **Linear Momentum** and provide its formula.

Accepted Answer

Linear Momentum ($\vec{p}$) is a measure of the mass in motion. It is the product of an object's mass and its velocity. It is a vector quantity.
**Formula:** $\vec{p} = m\vec{v}$
Where $m$ is mass and $\vec{v}$ is velocity. Its SI unit is kilogram-meters per second (kg·m/s).

Question 2

What is **Displacement**?

Accepted Answer

Displacement ($\Delta \vec{x}$ or $\Delta \vec{r}$) is the vector quantity representing the change in an object's position, from its initial to its final point. It includes both magnitude and direction. Its SI unit is meters (m).

Question 3

Define **Velocity** and provide its formula.

Accepted Answer

Velocity ($\vec{v}$) is the rate of change of an object's displacement with respect to time. It is a vector quantity.
*   **Average Velocity:** $\vec{v}_{avg} = \frac{\Delta \vec{x}}{\Delta t}$
*   **Instantaneous Velocity:** $\vec{v} = \frac{d\vec{x}}{dt}$
Its SI unit is meters per second (m/s).

Question 4

What is the difference between **Velocity** and **Speed**?

Accepted Answer

**Velocity** is a vector quantity that describes both the magnitude (speed) and direction of motion. **Speed** is a scalar quantity that only describes the magnitude of motion (how fast an object is moving), without regard to direction.

Question 5

Define **Acceleration** and provide its formula.

Accepted Answer

Acceleration ($\vec{a}$) is the rate of change of an object's velocity with respect to time. It is a vector quantity.
*   **Average Acceleration:** $\vec{a}_{avg} = \frac{\Delta \vec{v}}{\Delta t}$
*   **Instantaneous Acceleration:** $\vec{a} = \frac{d\vec{v}}{dt}$
Its SI unit is meters per second squared (m/s$^2$).

Question 6

List the primary **Kinematic Equations** for constant acceleration.

Accepted Answer

For constant acceleration ($\vec{a}$):
1.  $\vec{v} = \vec{v}_0 + \vec{a}t$
2.  $\Delta \vec{x} = \vec{v}_0t + \frac{1}{2}\vec{a}t^2$
3.  $v^2 = v_0^2 + 2a\Delta x$ (for 1D motion)
4.  $\Delta \vec{x} = \frac{1}{2}(\vec{v}_0 + \vec{v})t$
(Where $\vec{v}_0$ is initial velocity, $\vec{v}$ is final velocity, $t$ is time, $\Delta \vec{x}$ is displacement).

Question 7

State **Newton's First Law of Motion**.

Accepted Answer

Newton's First Law, also known as the Law of Inertia, states that 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.

Question 8

State **Newton's Second Law of Motion** and provide its formula.

Accepted Answer

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The direction of the acceleration is in the direction of the net force.
**Formula:** $\vec{F}_{net} = m\vec{a}$
Where $\vec{F}_{net}$ is the net force, $m$ is the mass, and $\vec{a}$ is the acceleration. Its SI unit is Newtons (N).

Question 9

State **Newton's Third Law of Motion**.

Accepted Answer

Newton's Third Law states that for every action, there is an equal and opposite reaction. If object A exerts a force on object B, then object B simultaneously exerts a force of equal magnitude and opposite direction on object A.

Question 10

Define **Force** and its SI unit.

Accepted Answer

Force ($\vec{F}$) is a push or a pull that can cause an object to accelerate (change its velocity). It is a vector quantity. Its SI unit is the Newton (N), where $1 \	ext{ N} = 1 \	ext{ kg} \cdot \	ext{m/s}^2$.

Question 11

Define **Mass** and its SI unit.

Accepted Answer

Mass ($m$) is a scalar measure of an object's inertia, or its resistance to changes in motion. It also quantifies the amount of matter in an object. Its SI unit is kilograms (kg).

Question 12

What is **Work** done by a constant force? Provide its formula and SI unit.

Accepted Answer

Work ($W$) is done when a force causes a displacement of an object. It is a scalar quantity.
**Formula:** $W = \vec{F} \cdot \Delta \vec{x} = F \Delta x \cos\	heta$
Where $F$ is the magnitude of the force, $\Delta x$ is the magnitude of the displacement, and $\	heta$ is the angle between the force and displacement vectors. Its SI unit is Joules (J), where $1 \	ext{ J} = 1 \	ext{ N} \cdot \	ext{m}$.

Question 13

State the **Work-Energy Theorem**.

Accepted Answer

The Work-Energy Theorem states that the net work done on an object is equal to the change in its kinetic energy.
**Formula:** $W_{net} = \Delta KE = KE_f - KE_i = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$

Question 14

Define **Kinetic Energy** and provide its formula.

Accepted Answer

Kinetic Energy ($KE$) is the energy an object possesses due to its motion. It is a scalar quantity.
**Formula:** $KE = \frac{1}{2}mv^2$
Where $m$ is the mass of the object and $v$ is its speed. Its SI unit is Joules (J).

Question 15

Define **Gravitational Potential Energy** and provide its formula.

Accepted Answer

Gravitational Potential Energy ($PE_g$) is the energy an object possesses due to its position in a gravitational field, relative to a reference point. It is a scalar quantity.
**Formula:** $PE_g = mgh$
Where $m$ is the mass, $g$ is the acceleration due to gravity (approx. $9.8 \	ext{ m/s}^2$ near Earth's surface), and $h$ is the height above the reference point. Its SI unit is Joules (J).

Question 16

What are **Conservative Forces** and **Non-Conservative Forces**?

Accepted Answer

*   **Conservative Forces:** Forces for which the work done in moving an object between two points is independent of the path taken (e.g., gravity, spring force). The work done in a closed loop is zero.
*   **Non-Conservative Forces:** Forces for which the work done depends on the path taken (e.g., friction, air resistance). They typically dissipate mechanical energy.

Question 17

State the **Law of Conservation of Mechanical Energy**.

Accepted Answer

In an isolated system where only conservative forces do work, the total mechanical energy ($E_{mech} = KE + PE$) of the system remains constant.
**Formula:** $KE_i + PE_i = KE_f + PE_f$
If non-conservative forces are present, $W_{nc} = \Delta E_{mech} = E_{mech,f} - E_{mech,i}$.

Question 18

Define **Power** and provide its formula and SI unit.

Accepted Answer

Power ($P$) is the rate at which work is done or energy is transferred. It is a scalar quantity.
**Formula:** $P = \frac{W}{\Delta t}$ or $P = \vec{F} \cdot \vec{v}$ (for constant force and velocity)
Its SI unit is Watts (W), where $1 \	ext{ W} = 1 \	ext{ J/s}$.

Question 19

Define **Impulse** and provide its formula.

Accepted Answer

Impulse ($\vec{J}$) is the change in momentum of an object. It is also defined as the product of the average net force acting on an object and the time interval over which the force acts. It is a vector quantity.
**Formula:** $\vec{J} = \vec{F}_{avg}\Delta t$
Its SI unit is Newton-seconds (N·s) or kilogram-meters per second (kg·m/s).

Question 20

State the **Impulse-Momentum Theorem**.

Accepted Answer

The Impulse-Momentum Theorem states that the impulse applied to an object is equal to the change in its linear momentum.
**Formula:** $\vec{J} = \Delta \vec{p} = \vec{p}_f - \vec{p}_i = m\vec{v}_f - m\vec{v}_i$

Question 21

State the **Law of Conservation of Linear Momentum**.

Accepted Answer

In an isolated system (where no external net forces act), the total linear momentum of the system remains constant.
**Formula:** $\sum \vec{p}_{initial} = \sum \vec{p}_{final}$
Or, for a two-object collision: $m_1\vec{v}_{1i} + m_2\vec{v}_{2i} = m_1\vec{v}_{1f} + m_2\vec{v}_{2f}$.

Question 22

Differentiate between **Elastic** and **Inelastic Collisions**.

Accepted Answer

*   **Elastic Collision:** A collision in which both momentum and kinetic energy are conserved. Objects bounce off each other without deformation or heat loss.
*   **Inelastic Collision:** A collision in which momentum is conserved, but kinetic energy is *not* conserved (some kinetic energy is converted to other forms, like heat or sound, or used for deformation). If objects stick together, it's a *perfectly inelastic collision*.

Classical Mechanics - Kinematics, Dynamics & Energy

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