Motion and Forces - Revision history

Conrad: Remove the Rows section (anchor names are documented on Template:Rt)

2026-10-25T21:52:20Z

Remove the Rows section (anchor names are documented on Template:Rt)

Conrad: Row anchors as zero-height blocks above the image, so a row link shows the whole table

2026-10-25T21:41:15Z

Row anchors as zero-height blocks above the image, so a row link shows the whole table

Conrad: Show the official table image instead of a wikitext copy; row anchors now land on the image

2026-10-25T21:39:58Z

Show the official table image instead of a wikitext copy; row anchors now land on the image

Conrad: Make the Regents Exam Questions table scroll sideways on narrow screens instead of widening the page

2026-10-25T21:31:28Z

Make the Regents Exam Questions table scroll sideways on narrow screens instead of widening the page

Conrad: Physics reference tables (2025 Edition): new reference table page

2026-10-25T20:25:59Z

Physics reference tables (2025 Edition): new reference table page

New page

{{Physreftable
|name=Motion and Forces
|prev=Vectors
|next=Energy
|desc=Motion and Forces equations from the NYS Physics Reference Tables (2025 Edition): average velocity, acceleration, the constant-acceleration equations, Newton's second law, weight, impulse, momentum, universal gravitation, centripetal acceleration and circumference, with their variables.
}}
The '''Motion and Forces''' page of the ''Reference Tables for Physical Science: Physics'' (2025 Edition) is the mechanics equation sheet: twelve equations with the meaning of their variables. The kinematics equations, Newton's second law and weight support [[HS-PS2-1]]; impulse and momentum support [[HS-PS2-2]] and [[HS-PS2-3]]; universal gravitation supports [[HS-PS2-4]]. Every equation has its own row anchor, so a link can point at one equation.

<div style="display:flex;flex-wrap:wrap;gap:16px 32px;align-items:flex-start;">
<div style="min-width:0;">
{| class="wikitable" style="text-align:center;"
! Equations
|- id="average-velocity"
| style="padding:8px 16px;" | ''v'' = ''d''''t'' = ''v''f + ''v''i2
|- id="acceleration"
| style="padding:8px 16px;" | ''a'' = Δ''v''''t'' = ''v''f − ''v''i''t''
|- id="vf-vi-at"
| style="padding:8px 16px;" | ''v''f = ''v''i + ''at''
|- id="d-vit-at2"
| style="padding:8px 16px;" | ''d'' = ''v''i''t'' + ½''at''2
|- id="vf2-vi2-2ad"
| style="padding:8px 16px;" | ''v''f2 = ''v''i2 + 2''ad''
|- id="fnet-ma"
| style="padding:8px 16px;" | ''F''net = ''ma''
|- id="fg-mg"
| style="padding:8px 16px;" | ''F''g = ''mg''
|- id="impulse"
| style="padding:8px 16px;" | ''F''net''t'' = ''m''Δ''v''
|- id="momentum"
| style="padding:8px 16px;" | ''p'' = ''mv''
|- id="gravitation"
| style="padding:8px 16px;" | ''F''g = ''Gm''1''m''2''r''2
|- id="centripetal"
| style="padding:8px 16px;" | ''a''c = ''v''2''r''
|- id="circumference"
| style="padding:8px 16px;" | ''C'' = 2π''r''
|}
</div>
<div style="min-width:0;">
{| class="wikitable"
! Variables
|-
| ''a'' = acceleration
|-
| ''a''c = radial acceleration during circular motion
|-
| ''C'' = circumference
|-
| ''d'' = displacement ''or'' distance
|-
| ''F''g = weight ''or'' gravitational force
|-
| ''F''net = net force
|-
| ''g'' = acceleration due to gravity ''or'' gravitational field strength
|-
| ''G'' = universal gravitational constant
|-
| ''m'' = mass
|-
| ''p'' = momentum
|-
| ''r'' = radius ''or'' distance between centers
|-
| ''t'' = time interval
|-
| ''v'' = velocity ''or'' speed
|-
| ''v'' = average velocity ''or'' average speed
|-
| ''v''i = initial velocity ''or'' initial speed
|-
| ''v''f = final velocity ''or'' final speed
|-
| Δ = change
|}
</div>
</div>

== What the motion and forces page shows ==
'''Kinematics.''' The first five equations describe motion with constant acceleration. Average velocity is displacement over time, or the mean of the initial and final velocities; acceleration is the change in velocity over time; and the three equations that follow connect final velocity, displacement, time and acceleration so that any one can be found from the others. For a falling object ''a'' is ''g'' from the [[List of Physical Constants#gravity|List of Physical Constants]].

'''Forces.''' ''F''net = ''ma'' is Newton's second law and ''F''g = ''mg'' the weight of an object; forces at an angle are split into components with the [[Vectors]] relationships. The 2006 edition also listed the friction equation ''F''f = μ''F''N with a table of coefficients of friction, the spring force ''F''s = ''kx'' and the centripetal force ''F''c = ''ma''c; none of these is on the 2025 tables, so a question that needs a coefficient of friction or a spring constant supplies it.

'''Momentum.''' ''p'' = ''mv'' defines momentum, and ''F''net''t'' = ''m''Δ''v'' is the impulse–momentum relationship: a net force acting for a time changes an object's momentum. Together they are the tools for [[HS-PS2-2]] (momentum is conserved in a collision) and [[HS-PS2-3]] (a longer collision time means a smaller force).

'''Gravitation and circular motion.''' ''F''g = ''Gm''1''m''2/''r''2 is Newton's law of universal gravitation, with ''G'' from the constants list and ''r'' the distance between centers; it is the gravitational half of [[HS-PS2-4]], and has the same form as [[Electricity#coulomb|Coulomb's law]]. ''a''c = ''v''2/''r'' gives the acceleration of an object in uniform circular motion, and ''C'' = 2π''r'' the distance it covers in one revolution.

== Rows ==
Each row of the table has an anchor, so a link or an <code><nowiki>{{Rt}}</nowiki></code> chip ([[Template:Rt]]) can point at one equation or constant:
* <code>average-velocity</code> – v̄ = ''d''/''t''
* <code>acceleration</code> – ''a'' = Δ''v''/''t''
* <code>vf-vi-at</code> – ''v''f = ''v''i + ''at''
* <code>d-vit-at2</code> – ''d'' = ''v''i''t'' + ½''at''2
* <code>vf2-vi2-2ad</code> – ''v''f2 = ''v''i2 + 2''ad''
* <code>fnet-ma</code> – ''F''net = ''ma''
* <code>fg-mg</code> – ''F''g = ''mg''
* <code>impulse</code> – ''F''net''t'' = ''m''Δ''v''
* <code>momentum</code> – ''p'' = ''mv''
* <code>gravitation</code> – ''F''g = ''Gm''1''m''2/''r''2
* <code>centripetal</code> – ''a''c = ''v''2/''r''
* <code>circumference</code> – ''C'' = 2π''r''

== Regents Exam Questions ==
Released Regents questions that cannot be answered without this table, listed by exam. Each link opens the question with its answer key; the standard is the one the question assesses.

{| class="wikitable" style="width:100%; text-align:center"
! style="padding: 0.5em 1.5em;" | Exam
! style="padding: 0.5em 1.5em;" | Cluster
! style="padding: 0.5em 1.5em;" | Question
! style="padding: 0.5em 1.5em;" | Standard
! style="padding: 0.5em 1.5em;" | Row
|-
| rowspan="6" style="background-color:white;" | [[June 2026 Physics Exam|June 2026 Physics Regents]]
| style="background-color:white;" | [[Questions:Pendulum Motion|Pendulum Motion]]
| style="background-color:white;" | [[Questions:Pendulum Motion#q4|Question 4]]
| style="background-color:white;" | [[HS-PS2-1]]
| style="background-color:white;" | ''F''g = ''mg''
|-
| style="background-color:white;" | [[Questions:Motorcycle Helmets|Motorcycle Helmets]]
| style="background-color:white;" | [[Questions:Motorcycle Helmets#q3|Question 17]]
| style="background-color:white;" | [[HS-PS2-3]]
| style="background-color:white;" | ''F''net''t'' = ''m''Δ''v''
|-
| style="background-color:white;" | [[Questions:Motorcycle Helmets|Motorcycle Helmets]]
| style="background-color:white;" | [[Questions:Motorcycle Helmets#q4|Question 18]]
| style="background-color:white;" | [[HS-PS2-1]]
| style="background-color:white;" | ''F''net = ''ma''
|-
| style="background-color:white;" | [[Questions:Motorcycle Helmets|Motorcycle Helmets]]
| style="background-color:white;" | [[Questions:Motorcycle Helmets#q6|Question 20]]
| style="background-color:white;" | [[HS-PS2-3]]
| style="background-color:white;" | ''F''net = ''ma''
|-
| style="background-color:white;" | [[Questions:From Astro Blaster to Supernova|From Astro Blaster to Supernova]]
| style="background-color:white;" | [[Questions:From Astro Blaster to Supernova#q3|Question 38]]
| style="background-color:white;" | [[HS-PS2-2]]
| style="background-color:white;" | ''p'' = ''mv''
|-
| style="background-color:white;" | [[Questions:Charged Drops|Charged Drops]]
| style="background-color:white;" | [[Questions:Charged Drops#q5|Question 50]]
| style="background-color:white;" | [[HS-PS2-1]]
| style="background-color:white;" | ''F''net = ''ma''
|-
| rowspan="3" style="background-color:white;" | [[Physics Sample Question Clusters|Physics sample clusters]] (spring 2025)
| style="background-color:white;" | [[Questions:Sampler World Record Jumps|World Record Jumps]]
| style="background-color:white;" | [[Questions:Sampler World Record Jumps#q1|Question 1]]
| style="background-color:white;" | [[HS-PS2-1]]
| style="background-color:white;" | ''a'' = Δ''v''/''t''; ''F''net = ''ma''
|-
| style="background-color:white;" | [[Questions:Sampler World Record Jumps|World Record Jumps]]
| style="background-color:white;" | [[Questions:Sampler World Record Jumps#q2|Question 2]]
| style="background-color:white;" | [[HS-PS2-1]]
| style="background-color:white;" | v̄ = ''d''/''t''
|-
| style="background-color:white;" | [[Questions:Sampler World Record Jumps|World Record Jumps]]
| style="background-color:white;" | [[Questions:Sampler World Record Jumps#q3|Question 3]]
| style="background-color:white;" | [[HS-PS2-1]]
| style="background-color:white;" | ''v''f2 = ''v''i2 + 2''ad''
|}

@@ Line 7: / Line 7: @@
 The '''Motion and Forces''' page of the ''Reference Tables for Physical Science: Physics'' (2025 Edition) is the mechanics equation sheet: twelve equations with the meaning of their variables. The kinematics equations, Newton's second law and weight support [[HS-PS2-1]]; impulse and momentum support [[HS-PS2-2]] and [[HS-PS2-3]]; universal gravitation supports [[HS-PS2-4]]. Every equation has its own row anchor, so a link can point at one equation.
-<span id="average-velocity"></span><span id="acceleration"></span><span id="vf-vi-at"></span><span id="d-vit-at2"></span><span id="vf2-vi2-2ad"></span><span id="fnet-ma"></span><span id="fg-mg"></span><span id="impulse"></span><span id="momentum"></span><span id="gravitation"></span><span id="centripetal"></span><span id="circumference"></span>[[File:Motion and Forces.png|760px|class=img-fluid|alt=Motion and Forces from the Physics Reference Tables (2025 Edition)]]
+<div id="average-velocity"></div><div id="acceleration"></div><div id="vf-vi-at"></div><div id="d-vit-at2"></div><div id="vf2-vi2-2ad"></div><div id="fnet-ma"></div><div id="fg-mg"></div><div id="impulse"></div><div id="momentum"></div><div id="gravitation"></div><div id="centripetal"></div><div id="circumference"></div>
 == What the motion and forces page shows ==

← Older revision		Revision as of 21:52, 25 October 2026
Line 18:		Line 18:

	'''Gravitation and circular motion.''' ''F''<sub>g</sub> = ''Gm''<sub>1</sub>''m''<sub>2</sub>/''r''<sup>2</sup> is Newton's law of universal gravitation, with ''G'' from the constants list and ''r'' the distance between centers; it is the gravitational half of [[HS-PS2-4]], and has the same form as [[Electricity#coulomb\|Coulomb's law]]. ''a''<sub>c</sub> = ''v''<sup>2</sup>/''r'' gives the acceleration of an object in uniform circular motion, and ''C'' = 2π''r'' the distance it covers in one revolution.		'''Gravitation and circular motion.''' ''F''<sub>g</sub> = ''Gm''<sub>1</sub>''m''<sub>2</sub>/''r''<sup>2</sup> is Newton's law of universal gravitation, with ''G'' from the constants list and ''r'' the distance between centers; it is the gravitational half of [[HS-PS2-4]], and has the same form as [[Electricity#coulomb\|Coulomb's law]]. ''a''<sub>c</sub> = ''v''<sup>2</sup>/''r'' gives the acceleration of an object in uniform circular motion, and ''C'' = 2π''r'' the distance it covers in one revolution.
−
−	~~== Rows ==~~
−	~~A link or an <code><nowiki>{{Rt}}</nowiki></code> chip ([[Template:Rt]]) can point at one equation or constant with these anchors; each one lands on the table above:~~
−	* <code>average-velocity</code> – v̄ = ''d''/''t''
−	* <code>acceleration</code> – ''a'' = Δ''v''/''t''
−	* <code>vf-vi-at</code> – ''v''<sub>f</sub> = ''v''<sub>i</sub> + ''at''
−	* <code>d-vit-at2</code> – ''d'' = ''v''<sub>i</sub>''t'' + ½''at''<sup>2</sup>
−	* <code>vf2-vi2-2ad</code> – ''v''<sub>f</sub><sup>2</sup> = ''v''<sub>i</sub><sup>2</sup> + 2''ad''
−	* <code>fnet-ma</code> – ''F''<sub>net</sub> = ''ma''
−	* <code>fg-mg</code> – ''F''<sub>g</sub> = ''mg''
−	* <code>impulse</code> – ''F''<sub>net</sub>''t'' = ''m''Δ''v''
−	* <code>momentum</code> – ''p'' = ''mv''
−	* <code>gravitation</code> – ''F''<sub>g</sub> = ''Gm''<sub>1</sub>''m''<sub>2</sub>/''r''<sup>2</sup>
−	* <code>centripetal</code> – ''a''<sub>c</sub> = ''v''<sup>2</sup>/''r''
−	* <code>circumference</code> – ''C'' = 2π''r''

	== Regents Exam Questions ==		== Regents Exam Questions ==

@@ Line 7: / Line 7: @@
 The '''Motion and Forces''' page of the ''Reference Tables for Physical Science: Physics'' (2025 Edition) is the mechanics equation sheet: twelve equations with the meaning of their variables. The kinematics equations, Newton's second law and weight support [[HS-PS2-1]]; impulse and momentum support [[HS-PS2-2]] and [[HS-PS2-3]]; universal gravitation supports [[HS-PS2-4]]. Every equation has its own row anchor, so a link can point at one equation.
-<div style="display:flex;flex-wrap:wrap;gap:16px 32px;align-items:flex-start;">
+<span id="average-velocity"></span><span id="acceleration"></span><span id="vf-vi-at"></span><span id="d-vit-at2"></span><span id="vf2-vi2-2ad"></span><span id="fnet-ma"></span><span id="fg-mg"></span><span id="impulse"></span><span id="momentum"></span><span id="gravitation"></span><span id="centripetal"></span><span id="circumference"></span>[[File:Motion and Forces.png|760px|class=img-fluid|alt=Motion and Forces from the Physics Reference Tables (2025 Edition)]]
 == What the motion and forces page shows ==
@@ Line 88: / Line 19: @@
 == Rows ==
-Each row of the table has an anchor, so a link or an <code><nowiki>{{Rt}}</nowiki></code> chip ([[Template:Rt]]) can point at one equation or constant:
+A link or an <code><nowiki>{{Rt}}</nowiki></code> chip ([[Template:Rt]]) can point at one equation or constant with these anchors; each one lands on the table above:
 * <code>average-velocity</code> – v̄ = ''d''/''t''
 * <code>acceleration</code> – ''a'' = Δ''v''/''t''

@@ Line 105: / Line 105: @@
 Released Regents questions that cannot be answered without this table, listed by exam. Each link opens the question with its answer key; the standard is the one the question assesses.
 {| class="wikitable" style="width:100%; text-align:center"
 ! style="padding: 0.5em 1.5em;" | Exam
@@ Line 159: / Line 160: @@
 | style="background-color:white;" | ''v''<sub>f</sub><sup>2</sup> = ''v''<sub>i</sub><sup>2</sup> + 2''ad''
 |}