Physics Lecture Notes: Kinematics, Dynamics, and Gravitation

Comprehensive practice flashcards covering Kinematics, Newton's Laws of Motion, Work-Power-Energy, Gravitation, and Center of Mass based on lecture notes.

When is an object considered to be in motion?

An object is in motion if its position changes with respect to time.

What is the primary difference between distance and displacement?

Distance is a scalar quantity representing the actual length covered by an object ($\text{always positive}$), while displacement is a vector quantity representing the shortest distance between initial and final points ($\text{can be positive, negative, or zero}$).

How do you calculate the displacement of an object moving $30\text{ m}$ North and $40\text{ m}$ East?

Using the Pythagorean theorem: \text{Resultant} = \text{\sqrt{N^2 + E^2}} = \text{\sqrt{30^2 + 40^2}} = \text{\sqrt{900 + 1600}} = \text{\sqrt{2500}} = 50\text{ m}.

What is the formula for average speed?

$$\text{Average Speed} = \frac{\text{Total distance}}{\text{Total time}}$$

What is the formula for average speed when an object covers two equal halves of a distance with speeds $v_1$ and $v_2$?

$$V_{avg} = \frac{2v_1v_2}{v_1 + v_2}$$

Under what condition are Newton's equations of motion ($v = u + at$, etc.) valid?

These equations are only valid when acceleration ($a$) is constant.

What is the mathematical relationship for acceleration ($a$) in terms of velocity ($v$) and position ($x$)?

$$a = \frac{dv}{dt} = v \frac{dv}{dx}$$

What is the formula for maximum height ($H_{\max}$) and time to reach it ($T$) for an object thrown vertically upward with initial velocity $u$?

$H_{\max} = \frac{u^2}{2g}$ and $T = \frac{u}{g}$.

What is the ratio of distance traveled by a body in successive seconds ($1^{st}, 2^{nd}, 3^{rd}$) during free fall?

The distances follow the ratio of odd numbers: $1:3:5$.

Define the horizontal and vertical components of initial velocity in projectile motion.

The horizontal component is u_x = u \times \text{\cos(\theta)} (remains constant) and the vertical component is u_y = u \times \text{\sin(\theta)} (changes due to gravity).

What is the formula for the horizontal range ($R$) of a projectile?

R = \frac{u^2 \text{\sin(2\theta)}}{g}

At what angle ($\theta$) is the horizontal range of a projectile at its maximum?

\theta = 45^\text{\circ}

What is the equation of the trajectory for a projectile?

y = x \text{\tan(\theta)} \times \text{\left(1 - \frac{x}{R}\right)} or y = x \text{\tan(\theta)} - \frac{gx^2}{2u^2 \text{\cos^2(\theta)}}.

What is Inertia?

Inertia is the property of a material to resist a sudden change in its state of rest or motion. It is directly proportional to mass.

State Newton's Second Law of Motion in its most general vector form.

\text{\mathbf{F}} = \frac{d\text{\mathbf{p}}}{dt} = m \frac{d\text{\mathbf{v}}}{dt} + \text{\mathbf{v}} \frac{dm}{dt}

Convert $1\text{ Newton}$ to dyne.

$$1\text{ Newton} = 10^5\text{ dyne}$$

Why do Action and Reaction forces not cancel each other out according to Newton's Third Law?

They do not cancel because they act on two different bodies.

What is the apparent weight ($T$) of a person in a lift moving upwards with acceleration $a$?

$$T = m(g + a)$$

What is the formula for the acceleration ($a$) of a simple fixed pulley system with two masses $m_1$ and $m_2$ ($m_2 > m_1$)?

$$a = \frac{m_2 - m_1}{m_1 + m_2} \times g$$

What is a pseudo force?

A 'fake' force ($F_p = m \times a$) applied to an object when observed from a non-inertial (accelerating) frame of reference to satisfy Newton's laws.

What is the law of limiting friction?

f_r = \text{\mu} \times R, where \text{\mu} is the coefficient of friction and $R$ is the normal reaction.

What is the work done by a force when the angle between the force and displacement is 90^\text{\circ}?

W = Fs \text{\cos(90^\text{\circ})} = 0.

State the Work-Energy Theorem.

The work done by all forces on a body is equal to the change in its kinetic energy: W = \text{\Delta KE} = \frac{1}{2}m(v_f^2 - v_i^2).

What is the relationship between Kinetic Energy ($KE$) and Linear Momentum ($p$)?

$$KE = \frac{p^2}{2m}$$

What is the formula for the potential energy ($U$) stored in a stretched spring?

$U = \frac{1}{2}kx^2$, where $k$ is the spring constant and $x$ is the displacement.

State Newton's Universal Law of Gravitation.

The gravitational force between two masses is $F = \frac{Gm_1m_2}{r^2}$, where $G = 6.67 \times 10^{-11}\text{ Nm}^2\text{kg}^{-2}$.

Who discovered the value of the Universal Gravitational Constant ($G$)?

Henry Cavendish.

How does acceleration due to gravity ($g$) change with height ($h$) above the Earth's surface?

g' = g \times \text{\left(\frac{R}{R+h}\right)}^2; for small heights, g' \text{\approx} g \times \text{\left(1 - \frac{2h}{R}\right)}.

What is the escape velocity ($v_e$) from the Earth's surface?

v_e = \text{\sqrt{\frac{2GM}{R}}} = \text{\sqrt{2gR}}, which is approximately $11.2\text{ km/sec}$.

What is the orbital velocity ($v_o$) of a satellite close to the Earth's surface?

v_o = \text{\sqrt{\frac{GM}{R}}} = \text{\sqrt{gR}} \text{\approx} 7.9\text{ km/sec}.

State Kepler's Second Law regarding planetary motion.

The areal velocity of a planet remains constant ($\frac{dA}{dt} = \text{constant}$), meaning it covers equal areas in equal intervals of time.

What characterizes a perfectly inelastic collision?

After the collision, the two objects stick together and move with a common velocity; kinetic energy is not conserved, but momentum is.

Define the Coefficient of Restitution ($e$).

$e = \frac{\text{Velocity of Separation}}{\text{Velocity of Approach}} = \frac{v_2 - v_1}{u_1 - u_2}$.

What is the formula for the Center of Mass ($x_{com}$) of a system of discrete particles?

$$x_{com} = \frac{m_1x_1 + m_2x_2 + \text{\dots}}{m_1 + m_2 + \text{\dots}}$$

Where is the Center of Mass for a solid hemisphere and a hollow hemisphere?

For a solid hemisphere, it is at $\frac{3R}{8}$. For a hollow hemisphere, it is at $\frac{R}{2}$.