Difference between revisions of "Motion and Forces"

Latest revision as of 17:52, 25 October 2026

⇱ All Physics Reference Tables (2025 Edition)
← Vectors	Energy →

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.

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.

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 = μF_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_nett = mΔv 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 = Gm₁m₂/r² 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 Coulomb's law. a_c = v²/r gives the acceleration of an object in uniform circular motion, and C = 2πr the distance it covers in one revolution.

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.

Exam	Cluster	Question	Standard	Row
June 2026 Physics Regents	Pendulum Motion	Question 4	HS-PS2-1	F_g = mg
	Motorcycle Helmets	Question 17	HS-PS2-3	F_nett = mΔv
	Motorcycle Helmets	Question 18	HS-PS2-1	F_net = ma
	Motorcycle Helmets	Question 20	HS-PS2-3	F_net = ma
	From Astro Blaster to Supernova	Question 38	HS-PS2-2	p = mv
	Charged Drops	Question 50	HS-PS2-1	F_net = ma
Physics sample clusters (spring 2025)	World Record Jumps	Question 1	HS-PS2-1	a = Δv/t; F_net = ma
	World Record Jumps	Question 2	HS-PS2-1	v̄ = d/t
	World Record Jumps	Question 3	HS-PS2-1	v_f² = v_i² + 2ad

@@ 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;">
+<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>
-<div style="min-width:0;">
+[[File:Motion and Forces.png|760px|class=img-fluid|alt=Motion and Forces from the Physics Reference Tables (2025 Edition)]]
-{| class="wikitable" style="text-align:center;"
-! Equations
-|- id="average-velocity"
-| style="padding:8px 16px;" | <span style="text-decoration:overline;">''v''</span> = <span style="display:inline-block;vertical-align:middle;text-align:center;line-height:1.25;"><span style="display:block;border-bottom:1px solid currentColor;padding:0 3px;">''d''</span><span style="display:block;padding:0 3px;">''t''</span></span> = <span style="display:inline-block;vertical-align:middle;text-align:center;line-height:1.25;"><span style="display:block;border-bottom:1px solid currentColor;padding:0 3px;">''v''<sub>f</sub> + ''v''<sub>i</sub></span><span style="display:block;padding:0 3px;">2</span></span>
-|- id="acceleration"
-| style="padding:8px 16px;" | ''a'' = <span style="display:inline-block;vertical-align:middle;text-align:center;line-height:1.25;"><span style="display:block;border-bottom:1px solid currentColor;padding:0 3px;">Δ''v''</span><span style="display:block;padding:0 3px;">''t''</span></span> = <span style="display:inline-block;vertical-align:middle;text-align:center;line-height:1.25;"><span style="display:block;border-bottom:1px solid currentColor;padding:0 3px;">''v''<sub>f</sub> − ''v''<sub>i</sub></span><span style="display:block;padding:0 3px;">''t''</span></span>
-|- id="vf-vi-at"
-| style="padding:8px 16px;" | ''v''<sub>f</sub> = ''v''<sub>i</sub> + ''at''
-|- id="d-vit-at2"
-| style="padding:8px 16px;" | ''d'' = ''v''<sub>i</sub>''t'' + ½''at''<sup>2</sup>
-|- id="vf2-vi2-2ad"
-| style="padding:8px 16px;" | ''v''<sub>f</sub><sup>2</sup> = ''v''<sub>i</sub><sup>2</sup> + 2''ad''
-|- id="fnet-ma"
-| style="padding:8px 16px;" | ''F''<sub>net</sub> = ''ma''
-|- id="fg-mg"
-| style="padding:8px 16px;" | ''F''<sub>g</sub> = ''mg''
-|- id="impulse"
-| style="padding:8px 16px;" | ''F''<sub>net</sub>''t'' = ''m''Δ''v''
-|- id="momentum"
-| style="padding:8px 16px;" | ''p'' = ''mv''
-|- id="gravitation"
-| style="padding:8px 16px;" | ''F''<sub>g</sub> = <span style="display:inline-block;vertical-align:middle;text-align:center;line-height:1.25;"><span style="display:block;border-bottom:1px solid currentColor;padding:0 3px;">''Gm''<sub>1</sub>''m''<sub>2</sub></span><span style="display:block;padding:0 3px;">''r''<sup>2</sup></span></span>
-|- id="centripetal"
-| style="padding:8px 16px;" | ''a''<sub>c</sub> = <span style="display:inline-block;vertical-align:middle;text-align:center;line-height:1.25;"><span style="display:block;border-bottom:1px solid currentColor;padding:0 3px;">''v''<sup>2</sup></span><span style="display:block;padding:0 3px;">''r''</span></span>
-|- id="circumference"
-| style="padding:8px 16px;" | ''C'' = 2π''r''
-|}
-</div>
-<div style="min-width:0;">
-{| class="wikitable"
-! Variables
-|-
-| ''a'' = acceleration
-|-
-| ''a''<sub>c</sub> = radial acceleration during circular motion
-|-
-| ''C'' = circumference
-|-
-| ''d'' = displacement ''or'' distance
-|-
-| ''F''<sub>g</sub> = weight ''or'' gravitational force
-|-
-| ''F''<sub>net</sub> = 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
-|-
-| <span style="text-decoration:overline;">''v''</span> = average velocity ''or'' average speed
-|-
-| ''v''<sub>i</sub> = initial velocity ''or'' initial speed
-|-
-| ''v''<sub>f</sub> = final velocity ''or'' final speed
-|-
-| Δ = change
-|}
-</div>
-</div>
 == What the motion and forces page shows ==
@@ Line 86: / 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.
-== 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''<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 ==