Quick Revision Notes: Class 11 Physics

Chapter: Laws of Motion (गति के नियम)

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1. Introduction to Force (बल)

Force is an external push or pull that changes or tends to change the state of rest or uniform motion of a body, or its direction of motion.

• SI Unit: Newton (N) or $\text{kg}\cdot\text{m/s}^2$
• Dimensional Formula: $[M^1 L^1 T^{-2}]$

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2. Newton's Laws of Motion (न्यूटन के गति के नियम)

A. Newton's First Law of Motion (प्रथम नियम - Law of Inertia)

An object remains in a state of rest or of uniform motion in a straight line unless compelled by an external force to change that state.

• Inertia (जड़त्व): The inherent property of a body to resist any change in its state of rest or uniform motion. It depends directly on the mass of the object.

B. Newton's Second Law of Motion (द्वितीय नियम)

The rate of change of momentum of a body is directly proportional to the applied external force and takes place in the direction in which the force acts.

• Formula: $$\vec{F} = \frac{d\vec{p}}{dt}$$
• Since $\vec{p} = m\vec{v}$, for a constant mass: $$\vec{F} = m\vec{a}$$
• Impulse (आवेग): A large force acting for a very short interval of time. $$\text{Impulse } (J) = \vec{F} \times \Delta t = \Delta \vec{p} = \vec{p}_2 - \vec{p}_1$$

C. Newton's Third Law of Motion (तृतीय नियम)

To every action, there is always an equal and opposite reaction.

• Formula: $$\vec{F}{AB} = -\vec{F}{BA}$$ (Force exerted by body A on B = - Force exerted by body B on A)

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3. Conservation of Linear Momentum (रेखीय संवेग संरक्षण का सिद्धांत)

If no external force acts on a system of bodies, the total linear momentum of the system remains constant.

• Formula: $$\text{If } \vec{F}_{\text{ext}} = 0, \text{ then } \vec{p} = \text{constant}$$ $$m_1\vec{v}_1 + m_2\vec{v}_2 = \text{constant}$$

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4. Friction (घर्षण)

Friction is the opposing force that comes into play when one body moves or tends to move over the surface of another body.

• Static Friction ($f_s$): Self-adjusting force opposing impending motion. $$f_{s,\text{max}} = \mu_s R$$
• Kinetic Friction ($f_k$): Opposes actual relative motion between surfaces. $$f_k = \mu_k R$$
• Rolling Friction ($f_r$): Opposes rolling motion. $$f_r = \mu_r R$$ (Note: $\mu_s > \mu_k > \mu_r$, where $\mu$ = coefficient of friction, $R$ = Normal reaction)

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5. Motion of Objects in Special Cases (विशेष स्थितियों में गति)

A. Apparent Weight in a Lift (लिफ्ट में आभासी भार)

• Lift accelerating upward with acceleration $a$: $$R = m(g + a)$$
• Lift accelerating downward with acceleration $a$: $$R = m(g - a)$$
• Lift moving freely downward (free fall, $a = g$): $$R = 0 \quad (\text{Weightlessness / भारहीनता})$$

B. Motion of Connected Bodies (जुड़े हुए पिंडों की गति)

• Two masses $m_1$ and $m_2$ connected by a string passing over a frictionless pulley ($m_1 > m_2$):
  • Acceleration ($a$): $$a = \left(\frac{m_1 - m_2}{m_1 + m_2}\right)g$$
  • Tension in the string ($T$): $$T = \frac{2m_1 m_2}{m_1 + m_2}g$$

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6. Circular Motion (वृत्तीय गति)

A. Centripetal Force (अभिकेंद्री बल)

The force required to move a body uniformly in a circle, acting towards the center.

• Formula: $$F_c = \frac{m v^2}{r} = m \omega^2 r$$ (where $v$ = linear velocity, $\omega$ = angular velocity, $r$ = radius)

B. Motion on a Level Circular Road (समतल वृत्तीय सड़क पर वाहन की गति)

Maximum safe velocity ($v_{\text{max}}$) without skidding: $$v_{\text{max}} = \sqrt{\mu r g}$$

C. Bending of a Cyclist (साइकिल सवार का झुकना)

Angle of banking ($\theta$) with the vertical: $$\tan\theta = \frac{v^2}{rg}$$

D. Banking of Roads (सड़क का बैंकिग/ढलान)

To avoid wear and tear of tires, the outer edge of the road is raised.

• Without friction: $$\tan\theta = \frac{v^2}{rg}$$
• With friction ($\mu$): $$v_{\text{max}} = \sqrt{rg \left(\frac{\mu + \tan\theta}{1 - \mu\tan\theta}\right)}$$

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Key MP Board Exam Tips:

1. Derivations to practice: Newton's Second law as the real law ($F = ma$), Motion of connected masses over a pulley, and Banking of curved roads.
2. Numerical Focus: Numerical problems are frequently asked on $F = ma$, conservation of momentum (recoil of gun), apparent weight in lifts, and maximum speed on banked roads. Always write proper units.