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 +

+ Options: + + Example: + TEXT`/> + TEXT +

+ *For demonstration purposes, this links to a warning in the vectors page in dynamics. +

+
+ + +

+ Tag type: Example +

+ Options: + + Example: + TEXT`/> + TEXT +

+ *For demonstration purposes, this links to an example in the vectors page in dynamics. +

+
+

Tag type: Regular

diff --git a/src/pages/dyn/contact_and_rolling.astro b/src/pages/dyn/contact_and_rolling.astro index 3f20f7dd9..ea99d74bb 100644 --- a/src/pages/dyn/contact_and_rolling.astro +++ b/src/pages/dyn/contact_and_rolling.astro @@ -190,11 +190,11 @@ import CalloutContainer from "../../components/CalloutContainer.astro"

We begin by observing that the sign conventions in - Figure #rko-ff mean that + Figure #rko-ff mean that . Now rolling without slipping means the contact point \(A\) must instantaneously have zero velocity, so using #rkg-er gives: + href="/dyn/rigid_body_kinematics#rkg-er">#rkg-er gives: @@ -247,7 +247,7 @@ import CalloutContainer from "../../components/CalloutContainer.astro" By definition of non-slip rolling contact, the point of contact \(P\) has zero velocity. The acceleration can be computed from the center \(C\) with #rkg-e2: + href="/dyn/rigid_body_kinematics#rkg-e2">#rkg-e2:

diff --git a/src/pages/dyn/geometric_properties.astro b/src/pages/dyn/geometric_properties.astro index 3222209d6..6d370e578 100644 --- a/src/pages/dyn/geometric_properties.astro +++ b/src/pages/dyn/geometric_properties.astro @@ -105,7 +105,7 @@ import Row from "../../components/Row.astro"

- Where from the differential of #rcm-tm. Substituting in: + Where from the differential of #rcm-tm. Substituting in:

@@ -361,8 +361,8 @@ import Row from "../../components/Row.astro"

- The total mass of the plate is , and with the chosen configuration \(y_P = 0\). Thus: - + The total mass of the plate is , and with the chosen configuration \(y_P = 0\). Thus: +

@@ -383,7 +383,7 @@ import Row from "../../components/Row.astro"

- 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.

@@ -421,7 +421,7 @@ 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 @@ -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.

@@ -834,7 +834,7 @@ import Row from "../../components/Row.astro"

- 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 . The parallel axis theorem #rem-el now gives: @@ -963,7 +963,7 @@ import Row from "../../components/Row.astro"

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 .

@@ -1077,7 +1077,7 @@ import Row from "../../components/Row.astro"

To compute the integrals in #rem-ec it is convenient to switch to - cylindrical coordinates: + cylindrical coordinates:

@@ -1131,7 +1131,7 @@ import Row from "../../components/Row.astro"

To compute the integrals in #rem-ec it is convenient to switch to - spherical coordinates: + spherical coordinates:

@@ -1160,7 +1160,7 @@ import Row from "../../components/Row.astro"

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.

diff --git a/src/pages/dyn/momentum.astro b/src/pages/dyn/momentum.astro index e6533c41a..d2928001a 100644 --- a/src/pages/dyn/momentum.astro +++ b/src/pages/dyn/momentum.astro @@ -255,7 +255,7 @@ import Col from "../../components/Col.astro"

The cross product of a vector with itself is zero - (cross product self-annihilation). So the + (cross product self-annihilation). So the integral of is a constant, which is the initial angular momentum. Assuming this is zero, we arrive at the desired expression. @@ -299,7 +299,7 @@ import Col from "../../components/Col.astro"

- 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.

@@ -551,7 +551,7 @@ import InlineCanvas from "../../components/InlineCanvas.astro" Take to be a unit vector rotating in the 2D plane, making an angle of \(\theta\) with the \(x\)-axis, as in Figure #rkr-f2. Then: + href="#rkr-fe-c">#rkr-fe-c. Then: diff --git a/src/pages/dyn/rigid_body_kinematics.astro b/src/pages/dyn/rigid_body_kinematics.astro index 4f74c8c7f..0bbd60af7 100644 --- a/src/pages/dyn/rigid_body_kinematics.astro +++ b/src/pages/dyn/rigid_body_kinematics.astro @@ -229,7 +229,7 @@ import DisplayTable from "../../components/DisplayTable.astro" where the derivative of comes from the rotation formula, given that + href="/dyn/particle_kinematics/#rkr-ew">rotation formula, given that this offset vector is simply rotating with the rigid body.

@@ -246,7 +246,7 @@ import DisplayTable from "../../components/DisplayTable.astro"

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 , as this is always zero. @@ -415,7 +415,7 @@ import DisplayTable from "../../components/DisplayTable.astro" Evaluating #rkg-er and using the cross-product expression #rvv-e9 now gives the + href="/dyn/vector_calculus#rvv-e9">#rvv-e9 now gives the velocity expression: @@ -937,13 +937,13 @@ import DisplayTable from "../../components/DisplayTable.astro" We can use conservation of energy to obtain an expression for .

- 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 and : diff --git a/src/pages/dyn/steering_geometry.astro b/src/pages/dyn/steering_geometry.astro index 48b7b2313..9f76d1219 100644 --- a/src/pages/dyn/steering_geometry.astro +++ b/src/pages/dyn/steering_geometry.astro @@ -68,8 +68,10 @@ import DisplayTable from "../../components/DisplayTable.astro" -

  • Rigid bodies
  • -
  • Constrained motion
  • + diff --git a/src/pages/dyn/work_and_energy.astro b/src/pages/dyn/work_and_energy.astro index 030119f0d..ecd241d22 100644 --- a/src/pages/dyn/work_and_energy.astro +++ b/src/pages/dyn/work_and_energy.astro @@ -59,7 +59,7 @@ import Col from "../../components/Col.astro"

    - 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:

    @@ -105,7 +105,7 @@ import Col from "../../components/Col.astro"

    - 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:

    @@ -141,7 +141,7 @@ import Col from "../../components/Col.astro"

    - 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:

    @@ -238,7 +238,7 @@ import Col from "../../components/Col.astro"

    - 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:

    @@ -290,14 +290,14 @@ import Col from "../../components/Col.astro"

    - We start with the general expression #rem-eb: + We start with the general expression #rem-eb: where we integrate over the body with a location \(P\). We choose a point \(Q\) fixed to the body and - use #rkg-er to express the + use #rkg-er to express the velocity of \(P\) in terms of and \(\vec\omega\), giving @@ -317,7 +317,7 @@ import Col from "../../components/Col.astro" orthogonal distance to point \(P\) from the line through \(Q\) in direction , so - from #rem-ei we see that + from #rem-ei we see that the final integral above is the moment of inertia about the axis through @@ -333,7 +333,7 @@ import Col from "../../components/Col.astro" - +

    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