diff --git a/src/pages/about/docs.astro b/src/pages/about/docs.astro
index 4bf40d925..92a52c2ee 100644
--- a/src/pages/about/docs.astro
+++ b/src/pages/about/docs.astro
@@ -844,6 +844,38 @@ All titles should be done in sentence case.
+
+ Tag type: Warning
+
+ *For demonstration purposes, this links to a warning in the vectors page in dynamics.
+
+ Tag type: Example
+
+ *For demonstration purposes, this links to an example in the vectors page in dynamics.
+ Tag type: Regular
We begin by observing that the sign conventions in
- Figure #rko-ff mean that
+ Figure #rko-ff mean that
+
+ Example:
+
+
+ Example:
+
- Where
- The total mass of the plate is
- It is convenient to switch to cylindrical coordinates:
+ It is convenient to switch to cylindrical coordinates:
@@ -404,7 +404,7 @@ import Row from "../../components/Row.astro"
- The centers of mass listed below are all special cases of the basic shapes given in Section #rcm-bs. Other
+ The centers of mass listed below are all special cases of the basic shapes given in Section #rcm-bs. Other
special cases can be easily obtained by similar methods, or directly computing the integral.
- See example problem on how to derive it by directly computing the integrals.
+ See example problem on how to derive it by directly computing the integrals.
The other perhaps simpler approach is to let \(x_Q = 0\) in #rcm-et, which forms a right triangle if the configuration
@@ -444,7 +444,7 @@ import Row from "../../components/Row.astro"
- See example problem on how to derive it by directly computing the integrals.
+ See example problem on how to derive it by directly computing the integrals.
The other perhaps simpler approach is to let \(x_Q = 0\) in #rcm-et, which forms a right triangle if the configuration
@@ -473,7 +473,7 @@ import Row from "../../components/Row.astro"
- It is convenient to switch to cylindrical coordinates:
+ It is convenient to switch to cylindrical coordinates:
@@ -823,7 +823,7 @@ import Row from "../../components/Row.astro"
Use the answer to Example Problem #rem-xs and the parallel axis
+ href="#example_btn_rem-xs">#rem-xs and the parallel axis
theorem #rem-el.
- In Example Problem #rem-xs we
+ In Example Problem #rem-xs we
computed the moment of inertia of a square place
about the center to be
Recall that in Example Problem #rem-xs we computed the
+ href="#example_btn_rem-xs">#rem-xs we computed the
moment of inertia of a square place about the center
to be
To compute the integrals in #rem-ec it is convenient to switch to
- cylindrical coordinates:
+ cylindrical coordinates:
To compute the integrals in #rem-ec it is convenient to switch to
- spherical coordinates:
+ spherical coordinates:
The moments of inertia listed below are all special cases of
the basic shapes given in Section #rem-sb. Other special cases can be
+ href="#basic_shapes_moi">#rem-sb. Other special cases can be
easily obtained by similar methods.
The cross product of a vector with itself is zero
- (cross product self-annihilation). So the
+ (cross product self-annihilation). So the
integral of
- As stated in the warning at #rec-wm, the
+ As stated in the warning at #rec-wm, the
relationship between Newton's equations and linear momentum are
not applicable for a system whose mass is changing with time. To use
that relationship, a few things must be changed. Consider the figure
diff --git a/src/pages/dyn/particle_kinematics.astro b/src/pages/dyn/particle_kinematics.astro
index 56a526430..34cbd2d15 100644
--- a/src/pages/dyn/particle_kinematics.astro
+++ b/src/pages/dyn/particle_kinematics.astro
@@ -198,7 +198,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro"
Velocity and acceleration of various movements. Compare to
- Figure #rvc-fp.
+ Figure #rvc-fp.
Because cross products are not associative, it is very
+ href="/dyn/vector_calculus#warning_rvv-wc">not associative, it is very
important to compute the centripetal acceleration term
with the parentheses as shown. That is, we must not
compute
- Using the work-energy theorem:
+ Using the work-energy theorem:
The rod is sliding along frictionless surfaces, so there are no non-conservative forces present,
- and constraint forces do no work (See work done by a constraint force)
+ and constraint forces do no work (See work done by a constraint force)
Therefore:
@@ -1014,7 +1014,7 @@ import DisplayTable from "../../components/DisplayTable.astro"
- We added one more assumption to the ones made in #rkc-xcp. Namely, the rope can only slip.
+ We added one more assumption to the ones made in #rkc-xcp. Namely, the rope can only slip.
This simply means that the tension is the same at any point in the rope.
@@ -1052,7 +1052,7 @@ import DisplayTable from "../../components/DisplayTable.astro"
- We have 3 unknowns, 2 equations. We apply our constraint equation from #rkc-xcp to relate
+ We have 3 unknowns, 2 equations. We apply our constraint equation from #rkc-xcp to relate
the accelerations of
- Beginning with #ren-ec and generalizing it to one-dimensional displacement in the y-direction, the equation becomes:
+ Beginning with #ren-wc and generalizing it to one-dimensional displacement in the y-direction, the equation becomes:
- Since gravity only acts in one direction, we can simplify #ren-efp to:
+ Since gravity only acts in one direction, we can simplify #ren-efp to:
- Since the restoring force in a spring only acts in one direction, we can simplify #ren-efp to:
+ Since the restoring force in a spring only acts in one direction, we can simplify #ren-efp to:
- Using conservation of energy, and the fact that a vector dotted with itself equals its magnitude squared (see #rvi-eg), then:
+ Using conservation of energy, and the fact that a vector dotted with itself equals its magnitude squared (see #rvi-eg), then:
- We start with the general expression #rem-eb:
+ We start with the general expression #rem-eb:
where \(W\) is the work done by non-conservative forces. If non-conservative forces are not present, then
it becomes conservation of energy.
@@ -405,7 +405,7 @@ import Col from "../../components/Col.astro"
The rotation angle \(\theta\) is measured around the same