RBSE Class 11 Physics Notes Chapter 5 Laws of Motion

These comprehensive RBSE Class 11 Physics Notes Chapter 5 Laws of Motion will give a brief overview of all the concepts.

RBSE Class 11 Physics Chapter 5 Notes Laws of Motion

Force:
Force is the factor which changes the state of an object or tries to change it. Forces are mainly of following types:

• Contact forces
• Non-contact forces
• Internal forces
• External forces

Inertia:
Inertia is the property of an object due to which it opposes any change in its state. There are following three kinds of inertia according to states:

• Inertia of rest
• Inertia of motion
• Inertia of direction

Linear momentum:
Linear momentum of a moving body is defined by the product of its mass and its velocity. It is vector quantity and denoted by p.
\(\vec{p}=m \vec{v}\)

 

Newton’s laws of motion:
After experiments performed by Galileo, Newton presented following three laws of motion:
(i) First law of motion: In absence of external force, any object wants to remain in its own state i.e., it opposes any change in its state untill external force is applied. This law is . also known as law of inertia.

(ii) Second law of motion: According to this law, “Rate of change of momentum of a moving body is directly proportional to applied force and in same direction in which the force is applied”, i.e.,
\(\vec{F}=\frac{d \vec{p}}{d t}=m \vec{a}\)
On the basis of this law, the unit of force ‘Newtotv’ east he defcved,
F = ma
If m = 1 kg; o = 1 ms^-2, then F = IN
i.e., ‘IN is the force which can produce an acceleartion of 1 ms^-2 in an object of mass 1 kg.”

(iii) Third law of motion: According to this law, “Every action has its equal and opposite reaction and action and reaction forces act on different objects.”
i.e \(\overrightarrow{F_{12}}=-\overrightarrow{F_{21}}\)

Law of conservation of linear momentum:
According to this law, “In absence of external force, the linear momentum of a particle remains unchanged” i.e. \(\vec{p}=m \vec{v}\) = constant or m₁v₂ = m₂v₂
Similarly for system of n particles,
\(\overrightarrow{p_1}+\overrightarrow{p_2}+\ldots \ldots+\overrightarrow{p_n}\) = constant
or \(\overrightarrow{\Delta p_1}+\overrightarrow{\Delta p_2}+\ldots \ldots \ldots+\overrightarrow{\Delta p_n}\) =0 (zero)

Impulse:
Total effect of a force on the motion of an object is called impulse. It is denoted by I and it is vector quantity. Its value is obtained by
I - F.Δt or \(\vec{I}=\overrightarrow{\Delta p}\)
7. Impulse momentum theorem: According to this theorem, “Impulse of a force is equal to change in momentum due to force.” i. e.,
I = Δp = (p₂ - p₁)

Concurrent forces:
If the lines of action of all the forces acting on a body pass through a common point, then the forces are said to be concurrent forces.

Pulley:
Pulley is the device which is used to change the direction of the force. A stable pulley is supposed to be massless and frictionless. If a cord passes over the pulley, then tension in cord is same on both sides.

Pseudo force:
The forces which actually do not act on a body but due to non inertial frame of reference, they appear to be in action, are called pseudo forces. For example, centrifugal force in uniform circular motion.

Friction:
When an object slips on the surface of other object, then a force is developed between the contact surface and opposes the relative motion. This opposing force is called the force of friction.

Laws of limiting friction:
Maximum static force of friction is called limiting friction. There are two laws of limiting friction:
(i) Limiting force is directly proportional to normal reaction acting between the surfaces in contact and always in opposite direction of motion.
(ii) Limiting friction does not depend upon the shape and size of bodies.

Angle of friction:
In the situation of limiting friction the angle between resultant reaction force and normal reaction is called angle of friction. It is denoted by a and can be obtained by relation tana = ps, where ps is coefficient of static friction.

Centripetal force:
When an object moves on a circular path, then a force acts on it, directing towards the centre of the path. This force is called centripetal force. It is given by,
F_c = \(\frac{m v^2}{r}\) = rω² = r.\(\frac{4 \pi^2}{T^2} \)= r.4π²n²

Centrifugal force:
If any how the centripetal force acting on a particle moving on circular path, breaks down, then a force in opposite direction of centripetal force, is experienced. This force is centrifugal force. It is a psuedo force.

Conical pendulum:
When a heavy body is tried to rotate in horizontal circle,then due to weight of the body the cord does not remain horizontal. Therefore the motion of cord traces a cone. This system is called conical pendulum.

Centrifuge:
This is an apparatus which is used to seperate the heavy and light particles mixed in a liquid. It is based on centrifugal force.

Non-uniform circular motion:
In non-uniform circular motion, the speed of particle also remains changing. Therefore, there is tangential acceleration also in action on particle along with radial or centripetal acceleration. Therefore resultant acceleration is obtained by
a = \(\sqrt{a_R^2+a_T^2}\)

→ Linear momentum \(\vec{p}=m \vec{v}\)

→ Force\( \overrightarrow{F}=m \vec{a}\)

→ Weight of an object of mass m, W = mg

→ Components of force,
\( \overrightarrow{F}=m \vec{a}\)
(F_xî + F_yĵ + F_z k̂)= m(a_x î + a_y ĵ + a_z k̂)
∴ Components F_x = ma_x; F_y = ma_y; F_z = ma_z

→ Resultant force \(\vec{F}=\vec{F}_1+\vec{F}_2\) or m \(\vec{a}=m \overrightarrow{a_1}+m \overrightarrow{a_2}\)
∴ Resultant acceleration \(\vec{a}=\overrightarrow{a_1}+\overrightarrow{a_2}\)

→ Impulse I = F.Δt = Δp

→ According to law of conservation of linear momentum,
\(\vec{p}\) = constant or \(\overrightarrow{\Delta p}\) = 0 and m₁v₁ = m₂v₂

→ Velocity of recoil of a gun
V = \(\frac{m v}{M}\)
where m and M are the masses of bullet and gun. v and V are the velocities of the bullet and the gun.

→ Force acting in varying mass system, when velocity \(\vec{v}\) is constant,
\(\vec{F}=\vec{v} \frac{d m}{d t}\)

→ Power of motor in conveyor belt loading system.
P = v².\(\frac{d m}{d t}\)

→ Velocity of rocket, v_f = v_i + ulog_e\(\left(\frac{m_i}{m_f}\right)\)
If v_i = 0, then v_f = u log_e\(\left(\frac{m_i}{m_f}\right)\)
= 2.303 ulog₁₀ \(\left(\frac{m_i}{m_f}\right)\)

→ If a body is in equilibrium under influence of two concurrent forces \(\vec{F}_1\) and \(\vec{F}_2\), then
\(\vec{F}_1+\vec{F}_2\) = 0 or \(\vec{F}_1=-\vec{F}_2\)

→ For equilibrium under three concurrent forces,
\(\vec{F}_1+\vec{F}_2+\vec{F}_3\)= 0 or \(\vec{F}_3=-\left(\vec{F}_1+\vec{F}_2\right)\)
or F₃ = \(\sqrt{F_1^2+F_2^2+2 F_1 F_2 \cdot \cos \theta}\)

→ For motion of mass attached with a pulley
Acceleration a = \(\frac{\left(m_1-m_2\right) g}{\left(m_1+m_2\right)}\) and
tension T = \(\frac{2 m_1 m_2 g}{\left(m_1+m_2\right)}\)

→ Apparent weight in moving lift:

• When lift is stationary or moving with uniform velcoity then R = mg
• When lift moves upwards with uniform aceeleration, then R = m(g+a)
• When lift moves downwards with uniform acceleration, then R = m(g~ a)
• When the cords of the lift as broken, then R = 0

→ Limiting friction, F_s = µ_sR = µ_s.mg and coefficient of friction, µ_s = \(\frac{F_s}{R}\).

→ Dynamic friction force, F_k = µ_k.R = µ_k.mg

→ In angle of friction is a and coefficient of static friction be µ_s, then µ_s = tan α

→ In inclination of a plane with horizontal is β and angle of friction is α, then in situation of limiting friction, β = α.

→ Force applied on a block for upwards motion or inclined plane,
P = ma + µmg cos β + mg sin β
If α = 0, then P = µ mg cos β + mg sin β
Here β is the angle of inclination of the plane.

→ For applied force on the body for downward motion on inclined plane,
P = ma + µ mgcosβ - mg sin β
If α = 0, then P = µmgcosβ - mg sin β

→ Work done on horizontal plane by friction force
W = µmg.S

→ Relation between r and ω i.e v = rω

→ Relation among r, a and α i.e a = r α

→ Centripetal force, F_c = \(\frac{m v^2}{r}\) = mrω²
= mr.\(\frac{4 \pi^2}{T^2}\) = mr4π²n²

→ Time period of conical pendulum, T = 2π\(\sqrt{\frac{l \cos \theta}{g}}\)

→ On turn the inclination from vertical, tan θ = \(\frac{v^2}{r g}\)

→ If coefficient of state friction is µ_s, then µ_s = tan θ and v_max² = rg. tan θ = µ_s.rg or v_max = \(\sqrt{\mu_s r g}\)

→ If the elevation of road at turn be h and the width of the road be l, then
tan θ = \(\frac{v^2}{r g}=\frac{h}{l}\)

→ If the speed of the vehicle at turn is less than the safe speed, the friction will be effective upwards along the road. In this situation,
\(\frac{v^2}{r g}=\frac{f_s \cos \theta-R \sin \theta}{R \cos \theta+f_s \sin \theta}\), where f_s = µ_s.R

→ If velocity of vehicle on turn is greater than safe velocity, then friction will be effective to down ward direction along the road. Then
\(\frac{v^2}{r g}=\frac{R \sin \theta+\mu_s R \cos \theta}{R \cos \theta-\mu R \sin \theta}\)
∴ v = \(\sqrt{r g\left[\frac{\tan \theta+\mu}{1-\mu \tan \theta}\right]}\)

→ Rocket propulsion: The gases produced in the rocket due to combustion of fuel are rejected by nozzle with high velcoity, as a result rocket experiences a force of reaction in opposite direction and moves accordingly. It is called rocket propulsion.

→ Concurrent forces: If the lines of action of forces acting on a body pass through a common point, then the forces are called concurrent forces.

→ Pulley: Pulley is a device which is used to change the direction of force.

→ Frame of reference: The system, in which situated an observer takes observations, is called fame of reference.

→ Pseudo force: The forces which actually do not act on a body but due to non-inertial frame of reference, they appear to act on the body, are called pseudo forces. For example, centrifugal force in circular motion.