eifueo/docs/ce1/ece105.md

# ECE 105: Classical Mechanics

## Motion

Please see [SL Physics 1#2.1 - Motion](/g11/sph3u7/#21-motion) for more information.

## Kinematics

Please see [SL Physics 1#Kinematic equations](/g11/sph3u7/#kinematic-equations) for more information.

## Projectile motion

Please see [SL Physics 1#Projectile motion](/g11/sph3u7/#projectile-motion) for more information.

## Uniform circular motion

Please see [SL Physics 1#6.1 - Circular motion](/g11/sph3u7/#61-circular-motion) for more information.

## Forces

Please see [SL Physics 1#2.2 - Forces](/g11/sph3u7/#22-forces) for more information.

## Work

Please see [SL Physics 1#2.3 - Work, energy, and power](/g11/sph3u7/#23-work-energy-and-power) for more information.

## Momentum and impulse

Please see [SL Physics 1#2.4 - Momentum and impulse](/g11/sph3u7/#24-momentum-and-impulse) for more information.

The change of momentum with respect to time is equal to the average force **so long as mass is constant**.

$$\frac{dp}{dt} = \frac{mdv}{dt} + \frac{vdm}{dt}$$

Impulse is actually the change of momentum over time.

$$\vec J = \int^{p_f}_{p_i}d\vec p$$

## Centre of mass

The centre of mass $x$ of a system is equal to the average of the centre of masses of its components relative to a defined origin.

$$x_{cm} = \frac{m_1x_1 + m_2x_2 + ... + m_nx_n}{m_1 + m_2 + ... + m_n}$$

To determine the centre of mass of a system with a hole, the hole should be treated as negative mass. If the geometry of the system is **symmetrical**, the centre of mass is also symmetrical in the x and y dimensions.

For each mass, its surface density $\sigma$ is equal to:

$$
\sigma = \frac{m}{A} \\
m = \sigma A
$$

Holes have negative mass, i.e., $m = -\sigma A$.

For a **one-dimensional** hole, the linear mass density uses a similar formula:

$$
\lambda =\frac{m}{L} \\
\lambda = \frac{dm}{dx}
$$

This means that a hole in a rod can use a different formula:
$$x_{cm} = \frac{1}{M}\int^M_0 xdm$$