Students can go through AP Inter 1st Year Physics Notes 5th Lesson Laws of Motion will help students in revising the entire concepts quickly.

## AP Inter 1st Year Physics Notes 5th Lesson Laws of Motion

→ Newton’s First Law ot Morion : “Every body continues to be in its state of rest or of uniform motion in a straightline unless compelled by an external force to change that state”.

→ Newton’s Second Law of Motion: “The rate of change of momentum of a body is directly proportional to the external force applied and takes place in the same direction in which the external force is acting”,

→ Newton’s Third Law of Motion : “To every action there is an equal an opposite reaction.

→ Two objects connected by a cable, one object having horizontal motion and the other having vertical motion

Tension T = \(\frac{ m_1 m_2 }{m_1+m_2}\) g

→ Two objects of unequal suspended by a cable passing over a pulley (At wood’s machine) In this case Tension T = \(\frac{2 m_1 m_2 }{m_1+m_2}\) g

→ Resultant force F_{R} of two forces F_{1} and F_{2} acting on a body simultaneously making an angle θ with each other is F_{R} = \(\sqrt{\mathrm{F}_1^2+\mathrm{F}_2^2+2 \mathrm{~F}_1 \mathrm{~F}_2 \cos \theta}\)

→ When the lift moves up with an acceleration ‘a’ then reaction force R = mg(1 + \(\frac{\mathrm{a}}{\mathrm{g}}\))

→ When the lift moves downwards with an acceleration ‘a1 then Reaction force R = mg (1 – \(\frac{\mathrm{a}}{\mathrm{g}}\)).

→ When the lift is stationary or moves with uniform velocity then acceleration is zero and net force is zero.

→ Impulse ( I ) is the product of force and time of action of force and is equal to change in momentum of the body. I = mv – mu

→ When the resultant external force acting on a system is zero, the total momentum of the system remains constant. This is called law of conservation of linear momentum.

→ m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}

→ If a body displaces by the application of force, work is said to be done by the force.

→ Impulse = Force × time duration = Change in momentum.

→ Mass is the measure of inertia.

→ Momentum of a body is defined to be the product of its mass m and velocity v.

p = mv

→ Friction : It is the force which always opposes, the relative motion between two surfaces in contact. It acts parallel to the surfaces and opposite to the direction of motion.

→ Three kinds of friction :

a) Static friction: It is the frictional force acting, when there is no relative motion between the surfaces of the bodies. It is always equal to the applied force. Static friction is a self adjusting force. The maximum value of the static friction is called “limiting friction”, F_{s}.

b) Kinetic friction (F_{k}) : It is the frictional force present, when a body slides over the other body.

→ The resistance encountered by a body in static friction while tending to move under the action of an external force is. called static friction. It is always equal and opposite to the applied force till the static friction reaches a maximum value.

→ The resistance encountered by a sliding body on a surface is kinetic friction. The applied force required to keep the body moving with uniform velocity, under friction is numerically equal to the value of kinetic friction. It is in the opposite direction of relative velocity between the . bodies in contact.

→ The resistance encountered by a rolling body on a surface is known as rolling friction.

→ Normal reaction is the resultant contact force acting on a body placed on a rigid surface perpendicular to the plane of contact. It is equal to mg on a horizontal surface and mg cos 0 on an inclined plane where m is the mass of the body and 0 is the angle of inclination of the inclined plane.

→ Laws of friction : i) The frictional force is independent of the area of contact, ii) The frictional force is directly proportional to the normal reaction.

→ In case of static friction, the frictional force is limiting friction. Coefficient of static friction μ_{s} = \(\frac{\mathrm{f}_{\mathrm{L}}}{\mathrm{N}}\)

→ In case of dynamic friction, the frictional force is kinetic friction. Coefficient of dynamic friction m_{k} = \(\frac{f_k}{N}\)

→ Laws of rolling friction :

- The smaller the area of contact the lesser will be the rolling friction,
- The larger the radius of the rolling body, the lesser will be the rolling friction,
- The rolling friction is directly proportional to the normal reaction.

Coefficient of rolling friction, μ_{r}= \(\frac{\mathrm{f}_{\mathrm{r}}}{\mathrm{N}}\)

→ The angle made by the resultant of the normal reaction and the limiting friction with normal reaction is called angle of friction. Coefficient of static friction μ_{s} = tan θ.

→ Acceleration or a body on a rough horizontal force, a = \(\frac{P-f_k}{m}=\frac{p-\mu_k m g}{m}\) where P is the applied force and m is the mass of the body.

→ Angle of repose is defined as the angle of inclination of a plane with respect to horizontal for which the body will be in limiting equilibrium on the inclined plane. If a is the angle of repose μ_{s} = tan α.

→ When a body slides down an inclined plane of angle of inclination (θ) greater than the angle of repose (α) i.e., θ > α, the acceleration of the body, a = g (sin θ – μ_{k} cos θ).

→ When a body starting from rest slides down the inclined plane of length l, its final velocity v = \(\sqrt{\sqrt{2 g l(\sin \theta}-\mu_{\mathrm{k}} \cos \theta}\) and time taken to slide down t = \(\sqrt{\frac{2 l}{g\left(\sin \theta-\mu_k \cos \theta\right)}}\)

→ When a body is to be moved up a rough inclined plane with uniform velocity the force to be applied F = mg (sin θ + m_{k} cos θ).

→ The acceleration, velocity and time taken by a body sliding along & smooth horizontal surface can be obtained by putting μ_{k} = 0. i.e., a = g sin θ, v = \(\sqrt{2 g l \sin \theta}\) and t = \(\sqrt{\frac{2 l}{g \sin \theta}}\). The force to move up the plane with uniform velocity is F = mg sin θ.

→ Pulling is easier than pushing. The net pul ing force is given by

P = F(cos θ + μ_{k} sin θ) – μ_{R} mg and the net pushing force is given by P’ = F(cos θ – μ_{R} sin θ) – μ_{R} mg.

→ Pulling force F = \(\frac{W \sin \phi}{\cos (\theta-\phi)}\) and poshing mg. F’ = \(\frac{W \sin \phi}{\cos (\theta-\phi)}\) where W is the weight of body, Φ is the angle of friction and θ is the angle made by F with the horizontal.