Classical Mechanics - Kinematics, Dynamics & Conservation Laws Flashcards

Question 1

What is Kinematics?

Accepted Answer

Kinematics is the branch of classical mechanics that describes the motion of points, objects, and groups of objects without considering the causes of their motion (i.e., forces).

Question 2

Differentiate between Displacement and Distance.

Accepted Answer

Displacement ($\Delta x$) is a vector quantity representing the change in position from an initial point to a final point, including direction. Distance is a scalar quantity representing the total path length traveled, regardless of direction.

Question 3

Define average and instantaneous velocity and acceleration.

Accepted Answer

Average velocity ($\vec{v}_{avg}$) is total displacement divided by total time ($\Delta \vec{x} / \Delta t$). Instantaneous velocity ($\vec{v}$) is the velocity at a specific instant, the derivative of position with respect to time ($rac{d\vec{x}}{dt}$). Average acceleration ($\vec{a}_{avg}$) is total change in velocity divided by total time ($\Delta \vec{v} / \Delta t$). Instantaneous acceleration ($\vec{a}$) is the acceleration at a specific instant, the derivative of velocity with respect to time ($rac{d\vec{v}}{dt}$).

Question 4

State the first kinematic equation (constant acceleration).

Accepted Answer

The first kinematic equation relates final velocity ($v$), initial velocity ($v_0$), acceleration ($a$), and time ($t$):
$v = v_0 + at$

Question 5

State the second kinematic equation (constant acceleration).

Accepted Answer

The second kinematic equation relates final position ($x$), initial position ($x_0$), initial velocity ($v_0$), acceleration ($a$), and time ($t$):
$x = x_0 + v_0t + rac{1}{2}at^2$

Question 6

State the third kinematic equation (constant acceleration).

Accepted Answer

The third kinematic equation relates final velocity ($v$), initial velocity ($v_0$), acceleration ($a$), and displacement ($\Delta x = x - x_0$):
$v^2 = v_0^2 + 2a(x - x_0)$

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 mathematical form.

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.
Mathematically: $\Sigma \vec{F} = m\vec{a}$

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 on object A that is equal in magnitude and opposite in direction.

Question 10

Define Force and explain the purpose of a Free-Body Diagram.

Accepted Answer

Force is an interaction that, when unopposed, will change the motion of an object. It is a vector quantity. A Free-Body Diagram (FBD) is a visual tool used to analyze forces acting on a single object, isolating it from its environment and representing all external forces as vectors originating from the object's center of mass.

Question 11

Define Work done by a constant force and provide its formula.

Accepted Answer

Work ($W$) done by a constant force is defined as the product of the magnitude of the force, the magnitude of the displacement, and the cosine of the angle ($	heta$) between the force and displacement vectors.
$W = Fd \cos	heta$ (or $W = \vec{F} \cdot \vec{d}$)

Question 12

Define Kinetic Energy and provide its formula.

Accepted Answer

Kinetic energy ($K$) is the energy an object possesses due to its motion. It is a scalar quantity.
$K = rac{1}{2}mv^2$, where $m$ is mass and $v$ is speed.

Question 13

State the Work-Energy Theorem.

Accepted Answer

The Work-Energy Theorem states that the net work done on an object by all forces acting on it is equal to the change in its kinetic energy.
$W_{net} = \Delta K = K_f - K_i$

Question 14

Define gravitational and elastic potential energy, providing their formulas.

Accepted Answer

Gravitational potential energy ($U_g$) is the energy an object possesses due to its position in a gravitational field, relative to a reference point.
$U_g = mgh$, where $m$ is mass, $g$ is acceleration due to gravity, and $h$ is height.
Elastic potential energy ($U_s$) is the energy stored in an elastic material (like a spring) when it is stretched or compressed from its equilibrium position.
$U_s = rac{1}{2}kx^2$, where $k$ is the spring constant and $x$ is the displacement from equilibrium.

Question 15

State the principle of Conservation of Mechanical Energy and its formula.

Accepted Answer

The principle of Conservation of Mechanical Energy states that if only conservative forces (like gravity or spring force) do work, the total mechanical energy ($E$) of a system remains constant.
$E = K + U = 	ext{constant}$ (where $K$ is kinetic energy and $U$ is potential energy).
Thus, $K_i + U_i = K_f + U_f$.

Question 16

Define Linear Momentum and provide its formula.

Accepted Answer

Linear momentum ($\vec{p}$) is a measure of the mass in motion. It is a vector quantity, defined as the product of an object's mass and its velocity.
$\vec{p} = m\vec{v}$

Question 17

State the Impulse-Momentum Theorem.

Accepted Answer

The Impulse-Momentum Theorem states that the impulse ($\vec{J}$) applied to an object is equal to the change in its linear momentum ($\Delta \vec{p}$).
$\vec{J} = \vec{F}_{avg} \Delta t = \Delta \vec{p} = \vec{p}_f - \vec{p}_i$

Question 18

State the principle of Conservation of Linear Momentum.

Accepted Answer

The principle of Conservation of Linear Momentum states that if the net external force acting on a system of objects is zero, then the total linear momentum of the system remains constant.
$\Sigma \vec{p}_{initial} = \Sigma \vec{p}_{final}$

Question 19

Define Angular Momentum for a rigid body and provide its formula.

Accepted Answer

Angular momentum ($\vec{L}$) is the rotational equivalent of linear momentum. For a rigid body rotating about a fixed axis, it is the product of its moment of inertia ($I$) and its angular velocity ($\vec{\omega}$).
$\vec{L} = I\vec{\omega}$

Question 20

State the principle of Conservation of Angular Momentum.

Accepted Answer

The principle of Conservation of Angular Momentum states that if the net external torque acting on a system is zero, then the total angular momentum of the system remains constant.
$\Sigma \vec{L}_{initial} = \Sigma \vec{L}_{final}$

Question 21

Define Torque and provide its formula.

Accepted Answer

Torque ($\vec{	au}$) is the rotational equivalent of force. It is a measure of the force's tendency to cause an object to rotate about an axis or pivot. It is a vector quantity.
$\vec{	au} = \vec{r} 	imes \vec{F}$ or $	au = rF\sin	heta$, where $r$ is the distance from the pivot to the point where the force is applied, $F$ is the force, and $	heta$ is the angle between $\vec{r}$ and $\vec{F}$.

Question 22

Define Power and provide its formulas.

Accepted Answer

Power ($P$) is the rate at which work is done or energy is transferred. It is a scalar quantity.
$P = rac{W}{t}$ (Work per unit time)
$P = \vec{F} \cdot \vec{v}$ (Force times velocity, for constant force and velocity)

Classical Mechanics - Kinematics, Dynamics & Conservation Laws

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