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--- 183_notes:acceleration [2014/07/11 01:56] – [Why not just use change in momentum?] caballero
+++ 183_notes:acceleration [2021/02/04 23:22] – [Acceleration] stumptyl
@@ Line 5: / Line 5: @@
 ==== Newton's Second Law ====
-The Momentum Principle (or Newton's Second Law) is a quantitative description for how a system changes it momentum when the system experiences an external force. You might already know that another way to write this principle uses the concept of acceleration (how the velocity changes with time). Mathematically, we can write Newton's Second Law like this:
+The Momentum Principle (or Newton's Second Law) is a quantitative description for how a system changes its momentum when the system experiences an external force. You might already know that another way to write this principle uses the concept of acceleration (how the velocity changes with time). Mathematically, we can write Newton's Second Law like this:
 $$\vec{F}_{net} = m\:\vec{a} = \dfrac{\Delta\vec{p}}{\Delta t}$$
@@ Line 13: / Line 13: @@
 $$\vec{a} = \dfrac{\Delta\vec{p}}{m\:\Delta t}=\dfrac{m\Delta\vec{v}}{m\:\Delta t}=\dfrac{\Delta\vec{v}}{\Delta t}$$
-where the last two equals signs hold only if the mass of the system is not changing.
+__//where the last two equals signs hold only if the mass of the system is not changing.
+//__
 ==== Acceleration ====
-//Acceleration is a vector quantity that quantifies how quickly the velocity of a system is changing.//
+**Acceleration** is a vector quantity that quantifies how quickly the velocity of a system is changing. The units of acceleration are **meters per second per second** ($\dfrac{m}{s^2}$).
 The acceleration can be defined in two ways and each is useful in different problems or ways of thinking. From Newton's Second Law, we can obtain a definition using the net force,
@@ Line 23: / Line 23: @@
 $$\vec{a} = \dfrac{\vec{F}_{net}}{m}$$
-Notice that this means that the acceleration of system always points in the direction of the net force (because mass is always a positive quantity).
+//Notice that this means that the acceleration of system always points in the direction of the net force (because mass is always a positive quantity).//
-It can also be defined (as above) in terms of the change in velocity over time. If this change is calculated over a time interval ($\Delta t$), then you obtain the //average// acceleration,
+It can also be defined (as above) in terms of the change in velocity over time. If this change is calculated over a time interval ($\Delta t$), then you obtain the //average acceleration,//
 $$\vec{a}_{avg} = \dfrac{\Delta \vec{v}}{\Delta t} = \dfrac{\vec{v}_f - \vec{v}_i}{\Delta t}$$
-If we allow the time interval to shrink ([[:183_notes:displacement_and_velocity#speed_and_velocity|as we did with the average velocity]]), we obtain the instantaneous acceleration,
+If we allow the time interval to shrink ([[:183_notes:displacement_and_velocity#speed_and_velocity|as we did with the average velocity]]), we obtain //the instantaneous acceleration,
+//
+$$\vec{a} = \lim_{\Delta t \rightarrow 0}\vec{a}_{avg} = \lim_{\Delta t \rightarrow 0}\dfrac{\Delta \vec{v}}{\Delta t} = \dfrac{d\vec{v}}{dt}$$
-$$\vec{a} = \lim_{\Delta t \rightarrow 0}\vec{a}_{avg} = \lim_{\Delta t \rightarrow 0}\dfrac{\Delta \vec{v}}{\Delta t} = \dfrac{d\vec{v}}{dt}$$
-The units of acceleration are meters per second per second ($\dfrac{m}{s^2}$).
 ==== Why not just use change in momentum? ====