A net force of $6\,\mathrm{N}$ acts westward on a $2\,\mathrm{kg}$ cart. What is the cart’s acceleration?

$3\,\mathrm{m\,s^{-2}}$ westward

$3\,\mathrm{m\,s^{-2}}$ eastward

$12\,\mathrm{m\,s^{-2}}$ westward

$0.33\,\mathrm{m\,s^{-2}}$ westward

Two skaters push away from each other on a nearly frictionless surface. Which statement correctly describes the forces and resulting accelerations during the push?

The forces are equal and opposite on different skaters; the lighter skater has the greater acceleration.

The heavier skater exerts the greater force and therefore accelerates less.

The forces are equal and opposite, so both skaters have equal acceleration.

Each skater’s force acts on that same skater, so the forces cancel.

Two carts collide on a track where external forces can be neglected. During the collision, one cart’s momentum changes. What follows for the total momentum of the two-cart system?

The total momentum remains constant, although each cart’s momentum may change.

The total momentum must become zero during the collision.

Only the heavier cart’s momentum remains constant.

The total momentum changes whenever either cart changes momentum.

Cheat sheet

Laws of Motion on one page, for a last look before a test.

Laws of Motion

Q: What are the most important topics in Class 11 Physics Laws of Motion?

Newton's three laws, momentum and impulse, conservation of momentum, free-body diagrams, friction (static and kinetic) and circular motion on level and banked roads carry most of the weight. For JEE and NEET, practise friction on inclines and banking problems in particular.

Q: How do I draw a free-body diagram?

Choose one body as your system and draw it as a dot or box. Then add every external force acting on that body only, such as weight, normal reaction, tension and friction, each with its direction. Never include forces the body exerts on others, and never include both forces of an action-reaction pair.

Q: What is the difference between inertia and mass?

Inertia is the property of a body to resist a change in its state of rest or uniform motion. Mass is the quantity that measures this property, so a body with more mass has more inertia and accelerates less for the same net force.

Q: What is the difference between static and kinetic friction?

Static friction acts when there is no sliding. It adjusts to match the applied force, up to a maximum of $\mu_s N$. Kinetic friction acts once sliding begins and is roughly constant at $\mu_k N$, which is usually a little smaller. You can also make your own flashcards or quiz for any chapter in Classly.

Cheat sheetClass 11 · Physics

⚑ Panic box

Net force — $\sum \vec F_{\rm ext}=m\vec a$ ; use the vector sum of external forces

Static friction — $f_s\leq \mu_sN$ ; it is not automatically at its maximum

Action–reaction — equal and opposite, simultaneous, and on different bodies

Circular motion — inward resultant $=mv^2/r$ ; identify the real force supplying it

Momentum — conserved only for an isolated system

1. Laws and momentum

Inertia — resistance to a change in rest or uniform straight-line motion; mass measures inertia.
Newton’s first law — zero net external force → zero acceleration → rest or constant velocity.
Newton’s second law — net external force points along momentum’s rate of change: $\vec F_{\rm net}=\dfrac{d\vec p}{dt}$ .
Fixed mass — $\vec p=m\vec v$ ; $\vec F_{\rm net}=m\vec a$ .
Momentum — $\vec p=m\vec v$ , a vector; direction matters even when speed is constant.
Force unit — $1\ \mathrm N=1\ \mathrm{kg\,m\,s^{-2}}$ .
System of particles — $\vec F_{\rm net,ext}=M\vec a_{\rm CM}$ ; internal forces are excluded.
Local rule — force at an instant determines acceleration at that instant; past motion does not supply a force.

2. Impulse and interactions

Impulse — $\vec J=\displaystyle\int \vec F\,dt=\Delta\vec p$ ; for constant force, $\vec J=\vec F\Delta t$ .
Impulsive force — large force over a short interval; use momentum change when force and contact time are hard to separate.
Newton’s third law — $\vec F_{A\,by\,B}=-\vec F_{B\,by\,A}$ ; the pair acts simultaneously on different bodies.
Conservation of momentum — isolated system: $\sum \vec p_{\rm before}=\sum \vec p_{\rm after}$ ; valid for elastic and inelastic collisions.
Elastic collision — momentum conserved; kinetic energy is also conserved.

3. Forces and equilibrium

Force	What to recall	Watch out
Weight	$mg$ , vertically downward near Earth	Not the normal force
Normal reaction	Contact-force component perpendicular to surfaces	$N=mg$ only in specific equilibrium situations
Tension	Pull along a string; same throughout a negligible-mass string	Direction is along the string
Spring force	$\vec F=-k\vec x$ , for small extension/compression	Opposes displacement from natural length
Friction	Contact-force component parallel to surfaces	Opposes relative or impending relative motion
Buoyancy	Upward force equals weight of displaced fluid	Contact force from fluid
Gravity	Acts at a distance	Does not require contact
Viscous drag / air resistance	Contact forces from fluids	Oppose motion relative to fluid

Particle equilibrium — $\sum\vec F=0$ ; particle is at rest or moves with constant velocity.
Component test — $\sum F_x=\sum F_y=\sum F_z=0$ .
Three concurrent forces — $\vec F_1+\vec F_2+\vec F_3=0$ ; their directed vectors close a triangle.

4. Friction: limits and cases

Type	Rule	Use / distinction
Static	$0\leq f_s\leq\mu_sN$	Adjusts as needed; opposes impending relative motion
Limiting static	$f_{s,\max}=\mu_sN$	At the instant sliding is about to begin
Kinetic / sliding	$f_k=\mu_kN$	Opposes actual sliding; usually $\mu_k<\mu_s$
Rolling resistance	Much smaller than sliding friction in typical cases	Real rolling bodies still experience resistance

Coefficients depend on the surfaces; these friction relations are approximate and usually independent of apparent contact area.
Kinetic friction is nearly independent of speed.
Rough horizontal surface — $N=mg$ only if there is no vertical acceleration or other vertical force.
Incline at impending slide — $mg\sin\theta=f_{s,\max}$ , $N=mg\cos\theta$ → $\tan\theta_{\max}=\mu_s$ .
Accelerating floor/train — static friction can accelerate a box with it: $ma\leq\mu_sN$ ; if horizontal and $N=mg$ , $a_{\max}=\mu_sg$ .

5. Circular motion

Centripetal acceleration — $a_c=\dfrac{v^2}{r}$ , directed towards the centre.
Required inward resultant — $F_c=\dfrac{mv^2}{r}$ ; “centripetal force” names the role of the net inward force, not an extra force.
Level road — $N=mg$ ; static friction supplies the inward force → $\dfrac{mv^2}{r}\leq\mu_smg$ → $v_{\max}=\sqrt{\mu_srg}$ .
Banked road, no friction needed — $v_0=\sqrt{rg\tan\theta}$ .
Banked road, maximum speed before slipping — $v_{\max}=\sqrt{rg\,\dfrac{\tan\theta+\mu_s}{1-\mu_s\tan\theta}}$ (under the chapter’s banking/friction model).
At $v<v_0$ , friction acts up the slope; parking on the bank requires $\tan\theta\leq\mu_s$ .

6. Set-up for mechanics problems

Sketch the bodies, links and supports.
Choose one body or group as the system.
Draw its free-body diagram; include all external forces on it.
Mark known directions and magnitudes; leave others unknown.
Apply $\sum\vec F=m\vec a$ to each chosen system; pair interaction forces using the third law.

7. Traps

~~A force is needed to maintain uniform motion~~ → a net force is needed to change velocity; friction explains why motion often stops.
~~$f_s=\mu_sN$ in every static case~~ → $f_s$ self-adjusts up to that limit.
~~Action and reaction cancel on one body~~ → they act on different bodies; do not put both in one body’s free-body diagram.
~~Weight and normal are always equal and opposite~~ → only when the vertical force balance gives that result.
~~Centripetal force is an additional force~~ → identify the inward component/resultant of tension, gravity, friction, or another real force.
~~$\vec F=m\vec a$ means $m\vec a$ is another force~~ → $m\vec a$ is the net external force.
~~Zero velocity means zero force~~ → at a turning point, velocity can be zero while acceleration and force are non-zero.
~~Friction opposes an object’s motion~~ → it opposes actual or impending relative motion at the contact.
~~Use internal forces in the system’s net force~~ → internal action–reaction pairs cancel; sum external forces only.

⚑ Panic box

Net force — $\sum \vec F_{\rm ext}=m\vec a$; use the vector sum of external forces

Static friction — $f_s\leq \mu_sN$; it is not automatically at its maximum

Action–reaction — equal and opposite, simultaneous, and on different bodies

Circular motion — inward resultant $=mv^2/r$; identify the real force supplying it

Momentum — conserved only for an isolated system

1. Laws and momentum

Inertia — resistance to a change in rest or uniform straight-line motion; mass measures inertia.
Newton’s first law — zero net external force → zero acceleration → rest or constant velocity.
Newton’s second law — net external force points along momentum’s rate of change: $\vec F_{\rm net}=\dfrac{d\vec p}{dt}$.
Fixed mass — $\vec p=m\vec v$; $\vec F_{\rm net}=m\vec a$.
Momentum — $\vec p=m\vec v$, a vector; direction matters even when speed is constant.
Force unit — $1\ \mathrm N=1\ \mathrm{kg,m,s^{-2}}$.
System of particles — $\vec F_{\rm net,ext}=M\vec a_{\rm CM}$; internal forces are excluded.
Local rule — force at an instant determines acceleration at that instant; past motion does not supply a force.

2. Impulse and interactions

Impulse — $\vec J=\displaystyle\int \vec F,dt=\Delta\vec p$; for constant force, $\vec J=\vec F\Delta t$.
Impulsive force — large force over a short interval; use momentum change when force and contact time are hard to separate.
Newton’s third law — $\vec F_{A,by,B}=-\vec F_{B,by,A}$; the pair acts simultaneously on different bodies.
Conservation of momentum — isolated system: $\sum \vec p_{\rm before}=\sum \vec p_{\rm after}$; valid for elastic and inelastic collisions.
Elastic collision — momentum conserved; kinetic energy is also conserved.

3. Forces and equilibrium

Force	What to recall	Watch out
Weight	$mg$, vertically downward near Earth	Not the normal force
Normal reaction	Contact-force component perpendicular to surfaces	$N=mg$ only in specific equilibrium situations
Tension	Pull along a string; same throughout a negligible-mass string	Direction is along the string
Spring force	$\vec F=-k\vec x$, for small extension/compression	Opposes displacement from natural length
Friction	Contact-force component parallel to surfaces	Opposes relative or impending relative motion
Buoyancy	Upward force equals weight of displaced fluid	Contact force from fluid
Gravity	Acts at a distance	Does not require contact
Viscous drag / air resistance	Contact forces from fluids	Oppose motion relative to fluid

Particle equilibrium — $\sum\vec F=0$; particle is at rest or moves with constant velocity.
Component test — $\sum F_x=\sum F_y=\sum F_z=0$.
Three concurrent forces — $\vec F_1+\vec F_2+\vec F_3=0$; their directed vectors close a triangle.

4. Friction: limits and cases

Type	Rule	Use / distinction
Static	$0\leq f_s\leq\mu_sN$	Adjusts as needed; opposes impending relative motion
Limiting static	$f_{s,\max}=\mu_sN$	At the instant sliding is about to begin
Kinetic / sliding	$f_k=\mu_kN$	Opposes actual sliding; usually $\mu_k<\mu_s$
Rolling resistance	Much smaller than sliding friction in typical cases	Real rolling bodies still experience resistance

Coefficients depend on the surfaces; these friction relations are approximate and usually independent of apparent contact area.
Kinetic friction is nearly independent of speed.
Rough horizontal surface — $N=mg$ only if there is no vertical acceleration or other vertical force.
Incline at impending slide — $mg\sin\theta=f_{s,\max}$, $N=mg\cos\theta$ → $\tan\theta_{\max}=\mu_s$.
Accelerating floor/train — static friction can accelerate a box with it: $ma\leq\mu_sN$; if horizontal and $N=mg$, $a_{\max}=\mu_sg$.

5. Circular motion

Centripetal acceleration — $a_c=\dfrac{v^2}{r}$, directed towards the centre.
Required inward resultant — $F_c=\dfrac{mv^2}{r}$; “centripetal force” names the role of the net inward force, not an extra force.
Level road — $N=mg$; static friction supplies the inward force → $\dfrac{mv^2}{r}\leq\mu_smg$ → $v_{\max}=\sqrt{\mu_srg}$.
Banked road, no friction needed — $v_0=\sqrt{rg\tan\theta}$.
Banked road, maximum speed before slipping — $v_{\max}=\sqrt{rg,\dfrac{\tan\theta+\mu_s}{1-\mu_s\tan\theta}}$ (under the chapter’s banking/friction model).
At $v<v_0$, friction acts up the slope; parking on the bank requires $\tan\theta\leq\mu_s$.

6. Set-up for mechanics problems

Sketch the bodies, links and supports.
Choose one body or group as the system.
Draw its free-body diagram; include all external forces on it.
Mark known directions and magnitudes; leave others unknown.
Apply $\sum\vec F=m\vec a$ to each chosen system; pair interaction forces using the third law.

7. Traps

~~A force is needed to maintain uniform motion~~ → a net force is needed to change velocity; friction explains why motion often stops.
~~$f_s=\mu_sN$ in every static case~~ → $f_s$ self-adjusts up to that limit.
~~Action and reaction cancel on one body~~ → they act on different bodies; do not put both in one body’s free-body diagram.
~~Weight and normal are always equal and opposite~~ → only when the vertical force balance gives that result.
~~Centripetal force is an additional force~~ → identify the inward component/resultant of tension, gravity, friction, or another real force.
~~$\vec F=m\vec a$ means $m\vec a$ is another force~~ → $m\vec a$ is the net external force.
~~Zero velocity means zero force~~ → at a turning point, velocity can be zero while acceleration and force are non-zero.
~~Friction opposes an object’s motion~~ → it opposes actual or impending relative motion at the contact.
~~Use internal forces in the system’s net force~~ → internal action–reaction pairs cancel; sum external forces only.

Flashcards

10 cards on Laws of Motion. Flip them here, or read them all below.

Laws of Motion flashcards1 of 10

Say the answer in your head, then flip.

All 10 cards

1
Inertia is a body'sto any change in its state of rest or uniform motion.
Resistance. Mass is the measure of a body's inertia.
2
What happens to a body's acceleration when the net external force on it is zero?
It is zero, so the body stays at rest or keeps moving with constant velocity.
3
Linear momentum of a body is.
$\mathbf{p}=m\mathbf{v}$ , a vector in the direction of the velocity.$\mathbf{p}=m\mathbf{v}$, a vector in the direction of the velocity.
4
Newton's second law in momentum form is.
$\mathbf{F}=\frac{d\mathbf{p}}{dt}$ , the rate of change of momentum.$\mathbf{F}=\frac{d\mathbf{p}}{dt}$, the rate of change of momentum.
5
For a constant force acting over a time interval, impulse is.
$\mathbf{J}=\mathbf{F}\Delta t=\Delta\mathbf{p}$ $\mathbf{J}=\mathbf{F}\Delta t=\Delta\mathbf{p}$
6
Why does a cricketer draw their hands backward while catching a fast ball?
It increases the stopping time, so the average force needed for the same momentum change is smaller.
7
Why don't the two forces of a third-law pair cancel each other?
They act on different bodies, so they never cancel on either body's free-body diagram.
8
When is the total momentum of a system of interacting particles conserved?
When the system is isolated, that is, no net external force acts on it.
9
The magnitude of static friction obeys.
$f_s\leq\mu_s N$ ; it adjusts to the applied force up to this limit.$f_s\leq\mu_s N$; it adjusts to the applied force up to this limit.
10
The net inward force needed for uniform circular motion of radius $r$ is.
$F_c=\dfrac{mv^2}{r}$ , supplied by real forces such as tension, friction or gravity.$F_c=\dfrac{mv^2}{r}$, supplied by real forces such as tension, friction or gravity.

Quiz

5 questions, each with the reason behind its answer.

1 of 5

A puck glides across a perfectly smooth, level surface with constant velocity. If the horizontal push keeping it moving is removed, what happens next?

Answer key

1
A puck glides across a perfectly smooth, level surface with constant velocity. If the horizontal push keeping it moving is removed, what happens next?
Answer: B. It keeps moving at the same velocity.
With no horizontal net force, the puck has no horizontal acceleration, so its velocity remains unchanged.
2
A net force of $6\,\mathrm{N}$ acts westward on a $2\,\mathrm{kg}$ cart. What is the cart’s acceleration?A net force of $6,\mathrm{N}$ acts westward on a $2,\mathrm{kg}$ cart. What is the cart’s acceleration?
Answer: C. $3\,\mathrm{m\,s^{-2}}$ westward$3,\mathrm{m,s^{-2}}$ westward
Newton’s second law gives $a=F/m=6/2=3\,\mathrm{m\,s^{-2}}$ , in the direction of the net force.Newton’s second law gives $a=F/m=6/2=3,\mathrm{m,s^{-2}}$, in the direction of the net force.
3
Two skaters push away from each other on a nearly frictionless surface. Which statement correctly describes the forces and resulting accelerations during the push?
Answer: D. The forces are equal and opposite on different skaters; the lighter skater has the greater acceleration.
The skaters exert equal and opposite forces on one another. Since their masses differ, the same force magnitude produces different acceleration magnitudes; the lighter skater accelerates more.
4
Two carts collide on a track where external forces can be neglected. During the collision, one cart’s momentum changes. What follows for the total momentum of the two-cart system?
Answer: B. The total momentum remains constant, although each cart’s momentum may change.
The collision forces are internal to the two-cart system and occur as equal-and-opposite pairs. With no net external force, the system’s total momentum remains constant, although each cart’s momentum may change.
5
A box remains at rest when a small horizontal push is applied to it. The static friction on the box is equal in magnitude and opposite in direction to the push.
Answer: A. True
While the box stays at rest, the net horizontal force must be zero. Static friction adjusts to balance the applied push, provided the push does not exceed the maximum static friction.

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Questions about Laws of Motion

What are the most important topics in Class 11 Physics Laws of Motion?

Newton's three laws, momentum and impulse, conservation of momentum, free-body diagrams, friction (static and kinetic) and circular motion on level and banked roads carry most of the weight. For JEE and NEET, practise friction on inclines and banking problems in particular.

How do I draw a free-body diagram?

Choose one body as your system and draw it as a dot or box. Then add every external force acting on that body only, such as weight, normal reaction, tension and friction, each with its direction. Never include forces the body exerts on others, and never include both forces of an action-reaction pair.

What is the difference between inertia and mass?

Inertia is the property of a body to resist a change in its state of rest or uniform motion. Mass is the quantity that measures this property, so a body with more mass has more inertia and accelerates less for the same net force.

What is the difference between static and kinetic friction?

Static friction acts when there is no sliding. It adjusts to match the applied force, up to a maximum of $\mu_s N$ . Kinetic friction acts once sliding begins and is roughly constant at $\mu_k N$ , which is usually a little smaller. You can also make your own flashcards or quiz for any chapter in Classly.Static friction acts when there is no sliding. It adjusts to match the applied force, up to a maximum of $\mu_s N$. Kinetic friction acts once sliding begins and is roughly constant at $\mu_k N$, which is usually a little smaller. You can also make your own flashcards or quiz for any chapter in Classly.