Kinetics: the study of the relationship between force and motion
Every object continues in its state of rest or uniform motion in a straight line unless acted upon by a resultant force.
An object doesn’t need a force to move at constant velocity
🏋️♂️ Inertia: The resistance of an object to a change in its state of motion is called inertia
🚫 Inertial frame: A frame that has no acceleration (constant velocity only) [you can tell you are in an inertial frame if objects float relative to the environement🚀]
The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass. The direction of the acceleration is in the direction of the resultant force.
$$ a=\text{constant }F/m $$
1 Newton = force of an object(1kg mass; 1$ms^{-2}$ acceleration)
🛗 Example: $m_2>m_1$ Determine the tension T
We place the following equations:
$$ \begin{aligned} &T-m_1g=m_1a \\ &T-m_2g=-m_2a \\ &\rule{3.5cm}{1pt} \\ &a=\frac{m_2-m_1}{m_1+m_2}g \end{aligned} $$
Then we solve for T:
$$ \begin{aligned} T&=m_1(a+g) \\ &=m_1(\frac{m_2-m_1}{m_1+m_2}g+g) \\ T&=m_1\frac{2m_2}{m_1+m_2}g \end{aligned} $$
🚤 Applied in circular motion in polar coordinates:
centripedal force: $\vec a=a_r \hat r=-\frac{v^2}{r}\hat r$
With $F=ma$ we get $\vec F=m \vec a=-\frac{mv^2}{r} \hat{r}$
If two bodies exert forces on each other, the force exerted by body 2 on body 1 is equal in magnitude and opposite in direction to the force exerted by body 1 on body 2.