Laws Of Motion-FORMULA SHEETS | PHYSICS | NEET

Ruhul Amin Alig

Formula Sheet
8 min read

Laws Of Motion

- All the important formulas in one go
1
Momentum

$M o m e n t u m = M a s s \times V e l o c i t y$ $p = m v$
Units and Dimensions:
S.I unit: $k g . m . s^{- 1}$
c.g.s unit: $g . c m . s^{- 1}$
Dimensional Formula: $[M L T^{- 1}]$
2
Newton's Second Law

$F \propto \frac{d p}{d t}$ $F = k \frac{d p}{d t}$ , where k is constant of proportionality such that k=1
$F = m \frac{d v}{d t} = m a$
Units and Dimensions of force:
S.I unit: $1 N = 1 k g m s^{- 2}$
c.g.s unit: $1 d y n e = 1 g . c m . s^{- 2}$
$1 N = 1 0^{5} d y n e$
3
Impulse

If a very large force acts on an object for a very short duration, then the force is called impulsive force or impulse. $I m p u l s e, J = \int_{t_{i}}^{t_{f}} F d t = \int_{p_{i}}^{p_{f}} d p = △ p$
This leads to the impulse-momentum theorem: $J = △ p$
Units and Dimensions of impulse:
$k g . m . s^{- 1} o r N . s$
For constant force, $J = F \int_{t_{i}}^{t_{f}} d t = F (t_{f} - t_{i}) = F △ t$
For variable force, we can define,
$F_{a v g} = \frac{△ p}{△ t}$
Hence impulse can be written as $J = F_{a v g} △ t$
4
Newton's Third Law
5
Equilibrium of a particle under concurrent forces

Equilibrium of a particle in mechanics refers to the situation when the net external force on the particle is zero.
For two forces $F_{1}$ and $F_{2}$ acting on the same particle equilibrium requires
$F_{1} = F_{2}$
For three concurrent forces, $F_{1}$ , $F_{2}$ and $F_{3}$ , equilibrium requires
$F_{1} + F_{2} + F_{3} = 0$
Resolving the forces along X, Y and Z axes we can rewrite above equation as:
$F_{1 x} + F_{2 x} + F_{3 x} = 0$
$F_{1 y} + F_{2 y} + F_{3 y} = 0$
$F_{1 z} + F_{2 z} + F_{3 z} = 0$
Lami's Theorem for three concurrent forces
6
Free-Body Diagrams

Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation. A free-body diagram is a special example of the vector diagrams.
Examples:
A book is at rest on a tabletop. A free-body diagram for this situation looks like this
A gymnast holding onto a bar, is suspended motionless in mid-air. The bar is supported by two ropes that attach to the ceiling. Diagram the forces acting on the combination of gymnast and bar. A free-body diagram for this situation looks like this:
A flying squirrel is gliding (no wing flaps) from a tree to the ground at constant velocity. Consider air resistance. A free-body diagram for this situation looks like this:
A rightward force is applied to a book in order to move it across a desk with a rightward acceleration. Consider frictional forces. Neglect air resistance. A free-body diagram for this situation looks like this
A block on a ramp. A free-body diagram for this situation looks like this
WEDGE CONSTRAINT:
Components of velocity along perpendicular direction to the contact plane of the two objects is always equal if there is no deformations and they remain in contact.
7
Friction

Static friction
Static friction is a self adjusting force and its magnitude depends on the applied force.
$$0
where N is the normal force $μ_{s}$ is coefficient of static friction
If the applied force on a body exceeds $(F_{s})_{m a x}$ it begins to slide.
Kinetic Friction $F_{k} < = μ_{k} N$ where $μ_{k}$ is coefficient of kinetic friction
$μ_{k} < μ_{s}$
Angle of Friction
The angle of friction is defined as the angle between the normal force (N) and the resultant force (R) of normal force and maximum friction force( $(F_{s})_{m a x}$ )
$R = (f_{s})_{m a x}^{2} + N^{2}$
$tan θ = \frac{( f _{s} ) _{m a x}}{N} = μ_{s}$
Angle of Repose
The angle of repose is the angle of inclined plane with the horizontal such that an object placed on it
begins to slide.
When the body just begins to slide
$(f_{s})_{m a x} = m g sin θ$ ........(i)
$N = m g cos θ$ .....(ii)
From (i) and (ii)
$μ_{s} = tan θ$

Angle of Repose = Angle of friction
Acceleration of a body down a rough inclined plane
$a = g (g sin θ - μ cos θ)$
8
Circular Motion

Circular motion is described as a movement of an object while rotating along a circular path.
Average angular velocity = $w_{a v} = \frac{θ _{2} - θ _{1}}{t _{2} - t _{1}} = \frac{Δ θ}{Δ t}$
Average angular acceleration = $α_{a v} = \frac{w _{2} - w _{1}}{t _{2} - t _{1}} = \frac{Δ w}{Δ t}$

Banking of road
The phenomena in which the edges of the curved roads are raised above the inner edge to provide the necessary centripetal force to the vehicles so that they take a safe turn. The various terminologies used in the case of banking of roads are:
Banked Turn- It is defined as the turn or change of direction in which the vehicle inclines towards inside.
Bank Angle-The angle at which the vehicle is inclined is defined as the bank angle.
The velocity of a vehicle on a curved banked road
$v = \frac{r g ( t a n θ + μ _{s} )}{1 - μ _{s} t a n θ}$
For a given pair of roads, and tyre $μ_{s} = t a n λ$ , where $λ$ is the angle of friction, the velocity of a vehicle on a curved banked road is $v = r g t a n (θ + λ)$
The safe velocity on an unbanked road is given by the expression $v_{m a x} = μ r g$
The expression for the angle of banking of road is given by $θ = t a n^{- 1} \frac{v ^{2}}{r g}$
The expression for the safe velocity on the banked road is given by $v_{m a x} = r g t a n θ$
Centripetal Force $F = m v^{2} / r = m w^{2} r$

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