Frequently used basic physics equations



This Article is about frequently used . I have covered most of physics equations for class 11 and 12. Earlier I had made a physics formula diary  which has been available for free download.  Now this Physics formulas and concepts pdf is little bit detailed in nature and there are the times when you study and you want most of your formulas in a page or two. This is a Frequently used physics equations guide which you can print out and stick in front of your study desk for easy reference. You can use this for easy reference of formulas while solving physics problems.

1. Kinematics

These links give the detailed notes on the respective chapters

Motion in one DimensionMotion in a plane

Average Velocity and speed

    \[{v_{avg}} = {{\Delta s} \over {\Delta t}}\]

average speed

Instantaneous velocity and speed

v = \mathop {\lim }\limits_{\Delta t \to 0} {{\Delta s} \over {\Delta t}} = {{ds} \over {dt}}
Instantaneous speed or speed is the magnitude of the instantaneous velocity

here s is the displacement of the object and has only one component(out of x, y and z) for motion along straight line and has two components for motion in a plane.

Acceleration
Average acceleration

    \[{a_{avg}} = {{\Delta v} \over {\Delta t}}\]

Instantaneous acceleration

    \[a = \mathop {\lim }\limits_{\Delta t \to 0} {{\Delta v} \over {\Delta t}} = {{dv} \over {dt}}\]

Equations of motion (constant acceleration)

    \[v = {v_0} + at\]

    \[x = {x_0} + {v_0} + {1 \over 2}a{t^2}\]

    \[{v^2} = {v_0}^2 + 2a(x - {x_0})\]

    \[\overline v  = {1 \over 2}(v + {v_0})\]

Free fall acceleration

    \[v = {v_0} + gt\]

    \[x = {x_0} + {v_0} + {1 \over 2}g{t^2}\]

    \[{v^2} = {v_0}^2 + 2g(x - {x_0})\]

Projectiles

Horizontal distance

    \[x = {v_x}t\]

Horizontal velocity

    \[{v_x} = {v_{x0}}\]

Vertical distance

    \[y = {v_{yo}}t - {1 \over 2}g{t^2}\]

Vertical velocity

    \[{v_y} = {v_{y0}} - gt\]

Here,
{v_x} is the velocity along x-axis,
{v_{x0}} is the initial velocity along x-axis,
{v_y} is the velocity along y-axis,
{v_{y0}} is the initial velocity along y-axis.
g is the acceleration due to gravity and
t is the time taken.

Time of flight

    \[t = {{2{v_o}\sin \theta } \over g}\]

Maximum height reached

    \[H = {{v_0^2{{\sin }^2}\theta } \over {2g}}\]

Horizontal range

    \[R = {{v_0^2\sin 2\theta } \over g}\]

Here,

v_{0} is the initial Velocity,
{\sin \theta } is the component along y-axis,
{\cos \theta }  is the component along x-axis.

Uniform circular motion

Angular velocity

    \[\omega  = {{d\theta } \over {dt}}\]

where \theta is angle moved in radian’s

Relation between linear velocity, angular velocity and radius of circular motion

    \[v=r\omega\]

Angular acceleration

    \[\alpha  = {{d\omega } \over {dt}}\]

Centripetal acceleration

    \[{a_c} = {{{v^2}} \over r}\]

    \[{{\vec a}_c} =  - {\omega ^2}\vec r\]

2. Laws of motion and friction

Links to Full length notes on these chapters are given below
Laws of motionFriction

Newton’s second law of motion

    \[\sum F  = m\vec a\]

    \[\sum F  = {{d\vec p} \over {dt}}\]

Weight

    \[W=mg\]

Limiting friction

    \[{f_{ms}} = {\mu _s}N\]

where N is the normal contact force and \mu _s coefficient of static friction.

3. Work energy and power

Full notes on Work energy and power
Work Energy and power

Work

work done by the force F in in displacing the body through displacement d

    \[W = \vec F \cdot \vec s\]

    \[W = \left| {\vec F} \right|\left| {\vec s} \right|\cos \theta\]

Work done by variable force

    \[W = \int {\vec F \cdot d\vec s}\]

Kinetic Energy

    \[K = {1 \over 2}m{v^2}\]

Potential Energy

    \[\Delta U =  - \int {\vec F \cdot d\vec s}\]

    \[\vec F =  - \nabla U\]

    \[F(x) =  - {{dU(x)} \over {dx}}\]

Mechanical energy

    \[E = K + U\]

Gravitational Potential energy

    \[U = mgh\]

Potential energy of the spring

    \[F =  - kx\]

    \[U = {1 \over 2}k{x^2}\]

Power

    \[P = {{dW} \over {dt}}\]

    \[\overline P  = {{\Delta W} \over {\Delta t}}\]

    \[P = \vec F \cdot \vec v\]

4. Impulse and Momentum

This link have Impulse and linear momentum notes.
Impulse and Momentum

Momentum

    \[p = m\vec v\]

Impulse

    \[\vec I = \vec F({t_2} - {t_1})\]

    \[\vec I = \int\limits_{{t_1}}^{{t_2}} {\vec Fdt}\]

5. System of Particles and Collisions

Links to detailed notes on this chapter

System of Particles and Collisions

Center of mass position vector

    \[\vec R = {{\sum {{m_i}{{\vec r}_i}} } \over M}\]

Inelastic collision

While colliding if two bodies stick together then speed of the composite body is

    \[v = {{{m_1}{u_1} + {m_2}{u_2}} \over {{m_1} + {m_2}}}\]

Elastic collision in one dimension

Final velocities of bodies after collision are

    \[{v_1} = \left( {{{{m_1} - {m_2}} \over {{m_1} + {m_2}}}} \right){u_1} + \left( {{{2{m_2}} \over {{m_1} + {m_2}}}} \right){u_2}\]

    \[{v_2} = \left( {{{2{m_1}} \over {{m_1} + {m_2}}}} \right){u_1} + \left( {{{{m_2} - {m_1}} \over {{m_1} + {m_2}}}} \right){u_2}\]

also

    \[{u_1} - {u_2} = {v_2} - {v_1}\]

6. Rotational Mechanics

Rotational mechanics notes
Rotational mechanics

Angular Velocity

    \[\vec v = \vec \omega  \times \vec r\]

Angular acceleration

    \[\vec a = \vec \alpha  \times \vec r - {\omega ^2}\vec r\]

Angular momentum of system of n particles about the origin

    \[\vec L = \sum\limits_{i = 1}^n {{{\vec r}_i} \times } {{\vec p}_i}\]

    \[L = mvr\sin \theta\]

    \[\vec L = I\vec \omega\]

torque or moment of force on system of n particles about the origin

    \[\vec \tau  = \sum\limits_{i = 1}^n {{{\vec r}_i} \times } {{\vec F}_i}\]

    \[\tau  = rF\sin \theta\]

Equations of rotation

    \[\omega  = {\omega _0} + \alpha t\]

    \[\theta  = {\theta _0} + {\omega _0}t + {1 \over 2}\alpha {t^2}\]

    \[{\omega ^2} = \omega _0^2 + 2\alpha \left( {\theta  - {\theta _0}} \right)\]

    \[\bar \omega  = {1 \over 2}(\omega  + {\omega _0})\]

Moment of inertia

    \[I = \sum {m{r^2}}\]

Kinetic energy of rotation

    \[K = {1 \over 2}I{\omega ^2}\]

Gravitation

Universal gravitation

    \[F = G{{{m_1}{m_2}} \over {{r^2}}}\]

Orbital speed

    \[v = \sqrt {{{Gm} \over r}}\]

escape speed

    \[v = \sqrt {{{2Gm} \over r}}\]

Acceleration due to gravity

(1) at height h above the surface of earth

    \[{g_h} = {{G{m_e}} \over {R_e^2}}\left( {1 - {{2h} \over {{R_e}}}} \right)\]

(2) at depth d below earth’s surface

    \[{g_d} = {{G{m_e}} \over {R_e^2}}\left( {1 - {d \over {{R_e}}}} \right)\]

Gravitational potential energy

    \[V =  - G{{{m_1}{m_2}} \over r}\]

I really want to share this article with you people but this is not complete. Anyway I am posting it but will be completing it later on. In the mean time you can check these links for other downloads

  1. Electrostatics class 12 and iitjee summary (pdf download)
  2. Mathematics revision sheet for class 11 and class 12 physics
  3. Vector Algebra part 1
  4. Vector Algebra part 2

Note
Also there is a good article on
How to do the physics problems
So go through this article I am sure it will help you when you try to solve physics problems

Books recommended for JEE examination(Physics)

  1. University Physics for the JEE – Vol. I
  2. University Physics for the JEE Vol. II (PB)
  3. Concepts of Physics – Vol. 1
  4. Concepts Of Physics:(V. 2)
    basic physics equations
  5. IIT JEE Physics (1978-2015: 38 Years) Topic-wise Complete Solutions, Vol. 1
  6. IIT JEE Physics (1978-2015: 38 Years) Topic-wise Complete Solutions, Vol. 2

Important page that contains most of the physics notes for class 11 , class 12, JEE(main and advance) and other competitive exams. You can visit this page and find notes of the chapters along with assignments.
Physics Notes

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