Mechanics Concepts

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Questions and Answers

A particle moves under the influence of a central force. Which of the following quantities is necessarily conserved?

Kinetic energy
Total energy
Linear momentum
Angular momentum (correct)

A simple pendulum is released from an initial angle $\theta_0$. Assuming small angle oscillations, what is the approximate period of oscillation?

$2\pi \sqrt{L/g} (1 + \frac{1}{16} \theta_0^2)$
$2\pi \sqrt{L/g}$ (correct)
$2\pi \sqrt{g/L} (1 + \frac{1}{16} \theta_0^2)$
$2\pi \sqrt{g/L}$

A particle is subjected to a force $\mathbf{F} = -k\mathbf{r}$, where $k$ is a positive constant and $\mathbf{r}$ is the position vector. What type of motion does the particle exhibit?

Damped oscillation
Simple harmonic motion (correct)
Projectile motion
Uniform circular motion

A block of mass $m$ slides down an inclined plane with coefficient of kinetic friction $\mu_k$. What is the acceleration of the block?

$g(\sin\theta - \mu_k \cos\theta)$ (D) Signup and view all the answers

Two particles with masses $m_1$ and $m_2$ are connected by a massless string over a pulley. Assuming $m_1 > m_2$, what is the tension in the string?

$\frac{2m_1 m_2}{m_1 + m_2}g$ (C) Signup and view all the answers

A projectile is launched with an initial velocity $v_0$ at an angle $\theta$ with respect to the horizontal. What is the maximum height reached by the projectile?

$\frac{v_0^2 \sin^2\theta}{2g}$ (A) Signup and view all the answers

A rigid body is rotating about a fixed axis with angular velocity $\omega$. If the moment of inertia is $I$, what is its rotational kinetic energy?

$\frac{1}{2}I\omega^2$ (B) Signup and view all the answers

What is the reduced mass of a system of two particles with masses $m_1$ and $m_2$?

$\frac{m_1 m_2}{m_1 + m_2}$ (D) Signup and view all the answers

A particle of mass $m$ is moving in a potential $V(x) = \frac{1}{2}kx^2$. What is the frequency of small oscillations?

$\frac{1}{2\pi}\sqrt{\frac{k}{m}}$ (C) Signup and view all the answers

A hoop and a solid cylinder, both with mass $M$ and radius $R$, are released from rest at the top of an inclined plane. Which one reaches the bottom first, assuming they roll without slipping?

The solid cylinder (B) Signup and view all the answers

Flashcards

Classical Mechanics

The study of the motion of objects, specifically the relationships between force, matter, and motion.

Velocity

A vector quantity that describes the rate of change of an object's position with respect to time and a frame of reference.

Acceleration

A vector quantity that describes the rate of change of an object's velocity with respect to time.

Newton's First Law

Newton's First Law 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 a force.