PHYS101 - Classical Mechanics & Newtonian Dynamics Flashcards

Question 1

Kinematic Equation: Velocity-Time Relationship

Accepted Answer

$$v = v_0 + at$$

Relates final velocity ($v$), initial velocity ($v_0$), constant acceleration ($a$), and time ($t$).

Question 2

Kinematic Equation: Position-Time Relationship

Accepted Answer

$$x = x_0 + v_0t + \frac{1}{2}at^2$$

Relates final position ($x$), initial position ($x_0$), initial velocity ($v_0$), constant acceleration ($a$), and time ($t$).

Question 3

Kinematic Equation: Velocity-Position Relationship (Timeless Equation)

Accepted Answer

$$v^2 = v_0^2 + 2a\Delta x$$

Relates final velocity ($v$), initial velocity ($v_0$), constant acceleration ($a$), and displacement ($\Delta x$). Useful when time $t$ is unknown.

Question 4

Newton's First Law of Motion (Law of Inertia)

Accepted Answer

An object remains at rest or continues to move at a constant velocity unless acted upon by a net external force ($\sum \mathbf{F} = 0 \implies \mathbf{a} = 0$).

Question 5

Newton's Second Law of Motion

Accepted Answer

$$\sum \mathbf{F} = m\mathbf{a}$$

The net force acting on an object is equal to the product of its mass ($m$) and its acceleration ($\mathbf{a}$). Force and acceleration act in the same direction.

Question 6

Newton's Third Law of Motion

Accepted Answer

$$\mathbf{F}_{A \	ext{ on } B} = -\mathbf{F}_{B \	ext{ on } A}$$

When object A exerts a force on object B, object B exerts an equal and opposite force on object A. Action-reaction pairs act on *different* objects.

Question 7

Static Friction vs. Kinetic Friction

Accepted Answer

- **Static Friction ($f_s$):** Prevents relative motion; maximum magnitude is $f_{s,\	ext{max}} = \mu_s N$.
- **Kinetic Friction ($f_k$):** Opposes motion in progress; magnitude is $f_k = \mu_k N$.
Note: Typically $\mu_s > \mu_k$ for a given pair of surfaces.

Question 8

Centripetal Acceleration and Force

Accepted Answer

Acceleration directed toward the center of a circular path:
$$a_c = \frac{v^2}{r} = \omega^2 r$$

Corresponding centripetal force:
$$F_c = m a_c = \frac{m v^2}{r}$$

Question 9

Definition of Work ($W$)

Accepted Answer

$$W = \mathbf{F} \cdot \mathbf{d} = F d \cos\	heta$$

The scalar product of force vector $\mathbf{F}$ and displacement vector $\mathbf{d}$, where $\	heta$ is the angle between them. Measured in Joules ($J$).

Question 10

Work-Energy Theorem

Accepted Answer

$$W_{\	ext{net}} = \Delta K = K_f - K_i$$

The net work done on an object by all combined forces equals the change in its translational kinetic energy.

Question 11

Translational Kinetic Energy ($K$)

Accepted Answer

$$K = \frac{1}{2}m v^2$$

The kinetic energy of an object of mass $m$ moving at speed $v$. A scalar quantity measured in Joules ($J$).

Question 12

Gravitational Potential Energy ($U_g$)

Accepted Answer

$$U_g = m g h$$

The energy stored in an object of mass $m$ due to its height $h$ above a chosen reference level in a uniform gravitational field $g$.

Question 13

Hooke's Law and Elastic Potential Energy ($U_s$)

Accepted Answer

- **Hooke's Law:** $F_s = -kx$ (restoring force exerted by an ideal spring)
- **Elastic Potential Energy:** $$U_s = \frac{1}{2} k x^2$$
where $k$ is the spring constant and $x$ is displacement from equilibrium.

Question 14

Linear Momentum ($p$) and Impulse ($J$)

Accepted Answer

- **Linear Momentum:** $p = m v$
- **Impulse:** $J = \Delta p = \int F \, dt = F_{\	ext{avg}} \Delta t$

Impulse is the net force applied over time and equals the change in linear momentum.

Question 15

Conservation of Linear Momentum

Accepted Answer

If no net external force acts on a system ($\sum \mathbf{F}_{\	ext{ext}} = 0$), total linear momentum is conserved:
$$\mathbf{p}_{\	ext{initial}} = \mathbf{p}_{\	ext{final}}$$

Question 16

Elastic vs. Inelastic Collisions

Accepted Answer

- **Elastic Collision:** Linear momentum and total kinetic energy are both conserved ($K_i = K_f$).
- **Inelastic Collision:** Linear momentum is conserved, but kinetic energy is *not* conserved ($K_i \
eq K_f$).
- **Completely Inelastic Collision:** Objects stick together after impact, maximizing kinetic energy loss.

Question 17

Torque ($\	au$)

Accepted Answer

$$\mathbf{\	au} = \mathbf{r} \	imes \mathbf{F} \implies \	au = r F \sin\	heta$$

The rotational equivalent of force, measuring the tendency of a force to cause rotation about a pivot. $r$ is position vector from pivot, $\	heta$ is angle between $\mathbf{r}$ and $\mathbf{F}$.

Question 18

Rotational Kinematic Variables & Linear Analogies

Accepted Answer

- Angular Displacement $\	heta \leftrightarrow x$ (Displacement)
- Angular Velocity $\omega = \frac{d\	heta}{dt} \leftrightarrow v$ (Velocity)
- Angular Acceleration $\alpha = \frac{d\omega}{dt} \leftrightarrow a$ (Acceleration)

Tangential relationships: $x = r\	heta$, $v_t = r\omega$, $a_t = r\alpha$.

Question 19

Moment of Inertia ($I$)

Accepted Answer

$$I = \sum m_i r_i^2 \quad \	ext{or} \quad I = \int r^2 \, dm$$

The rotational analog of mass; quantifies an object's resistance to angular acceleration depending on mass distribution relative to the axis of rotation.

Question 20

Newton's Second Law for Rotation

Accepted Answer

$$\sum \	au = I \alpha$$

The net torque acting on a rigid body is equal to the product of its moment of inertia ($I$) and its angular acceleration ($\alpha$).

Question 21

Rotational Kinetic Energy ($K_{\	ext{rot}}$)

Accepted Answer

$$K_{\	ext{rot}} = \frac{1}{2} I \omega^2$$

The kinetic energy due to rotation. For a rolling object without slipping, total kinetic energy is:
$$K_{\	ext{total}} = \frac{1}{2} m v_{\	ext{cm}}^2 + \frac{1}{2} I_{\	ext{cm}} \omega^2$$

Question 22

Angular Momentum ($L$) and Conservation

Accepted Answer

- **Angular Momentum:** $L = I \omega$ (or $\mathbf{L} = \mathbf{r} \	imes \mathbf{p}$)
- **Conservation of Angular Momentum:** If $\sum \	au_{\	ext{ext}} = 0$, then $L_{\	ext{initial}} = L_{\	ext{final}}$ ($I_i \omega_i = I_f \omega_f$).

PHYS101 - Classical Mechanics & Newtonian Dynamics

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