Laws of Motion — Class 11 Physics

1. Force and Inertia

Force is an interaction that can change an object’s state of motion or shape. Inertia is the tendency of an object to resist a change in its state of motion. Mass is a quantitative measure of inertia.

2. Newton’s First Law

An object remains at rest or continues in uniform straight-line motion unless acted upon by a net external force. This law establishes the idea of inertia and identifies inertial frames of reference.

3. Newton’s Second Law

The net external force equals the rate of change of momentum: F_net=dp/dt. For constant mass, this becomes F_net=ma. Acceleration is in the direction of the net force.

4. Newton’s Third Law

Forces always occur in interaction pairs. If object A exerts a force on B, B simultaneously exerts an equal-magnitude, opposite-direction force on A. The two forces act on different bodies, so they do not cancel each other on one free-body diagram.

5. Momentum and Impulse

Linear momentum is p=mv. Impulse is the change in momentum: J=Δp=FΔt for constant force, or more generally the area under a force-time graph. In an isolated system, total linear momentum is conserved.

6. Free-Body Diagrams

A free-body diagram isolates one object and shows only the external forces acting on it. Common forces are weight mg downward, normal reaction N perpendicular to a contact surface, tension T along a string, and friction along the contact surface.

7. Friction

Static friction adjusts up to a limiting value: f_s≤μ_sN. Kinetic friction during sliding is approximately f_k=μ_kN. Friction opposes relative motion or the tendency of relative motion, not necessarily the direction of an object’s velocity.

8. Circular Motion and Force

For circular motion, the net radial force must provide centripetal acceleration: F_c=mv²/r. “Centripetal force” is not a new fundamental force; it is the name given to the net inward force required for circular motion. Gravity, tension, friction or a combination may provide it.

Worked Numerical 1 — Newton’s Second Law

Question: A net force of 20 N acts on a 5 kg block on a smooth horizontal surface. Find its acceleration.

Solution: F=ma, so a=F/m=20/5=4 m/s².

Worked Numerical 2 — Two Opposing Forces

Question: A 10 kg trolley is pulled by 50 N to the right while a 20 N force acts to the left. Find acceleration.

Taking right as positive, F_net=50−20=30 N. Therefore a=30/10=3 m/s² to the right.

Worked Numerical 3 — Block on a Rough Horizontal Surface

Question: A 5 kg block is pulled horizontally by 20 N. If μ_k=0.2 and g=10 m/s², find its acceleration.

N=mg=50 N. Kinetic friction=μ_kN=0.2×50=10 N.

Net force=20−10=10 N. Therefore a=10/5=2 m/s².

Worked Numerical 4 — Tension in a Vertical Lift

Question: A 10 kg object is lifted upward with acceleration 2 m/s². Take g=10 m/s². Find the tension.

Forces: T upward and mg downward. T−mg=ma.

T=m(g+a)=10(10+2)=120 N.

Worked Numerical 5 — Impulse

Question: A 0.2 kg ball changes velocity from 5 m/s east to 15 m/s west. Find the impulse.

Take east as positive. Initial velocity u=+5 m/s and final velocity v=−15 m/s.

J=Δp=m(v−u)=0.2(−15−5)=−4 N·s. The impulse has magnitude 4 N·s toward the west.

Worked Numerical 6 — Circular Motion

Question: A 1000 kg car moves at 10 m/s around a circular path of radius 50 m. Find the required centripetal force.

F=mv²/r=1000×100/50=2000 N, directed toward the centre.

Explained MCQs

1. An object moves at constant velocity. What is the net external force?
   Answer: Zero. Constant velocity means zero acceleration, so Newton’s second law gives F_net=0.
2. Action and reaction forces do not cancel each other because:
   Answer: They act on different bodies. A free-body diagram of one object contains only forces acting on that object.
3. Static friction is always equal to μ_sN.
   Answer: False. Static friction can take any value up to the limiting value μ_sN, depending on the applied force.
4. If the net force on an object is doubled while mass remains constant, acceleration:
   Answer: Doubles. From a=F/m.
5. Which force can provide centripetal force for a satellite orbiting Earth?
   Answer: Gravitational force. Gravity supplies the required inward net force.
6. Friction always acts opposite to:
   Answer: Relative motion or its tendency between surfaces. It does not necessarily oppose the overall motion of the object.

Competency Question

A passenger standing in a bus tends to lean backward when the bus suddenly accelerates forward. Explain this using inertia and Newton’s first law.

HOTS

A book rests on a horizontal table. The book exerts a downward force on the table and the table exerts an upward normal force on the book. Are these two forces an action-reaction pair? Explain which bodies each force acts on.

Free-Body Diagram Checklist

1. Choose and isolate one object.
2. Draw only external forces acting on that object.
3. Choose positive directions.
4. Resolve forces into components if necessary.
5. Apply ΣF=ma separately along each relevant direction.

Common Mistakes

• Thinking action and reaction act on the same object.
• Assuming static friction is always μ_sN.
• Calling centripetal force an additional force instead of identifying the actual inward force.
• Forgetting the direction of acceleration.
• Putting forces exerted by the object itself on its own free-body diagram.

Quick Revision

• p=mv
• F_net=dp/dt; for constant mass F=ma
• Impulse J=Δp
• Weight W=mg
• f_s≤μ_sN
• f_k=μ_kN
• F_centripetal=mv²/r
• Always identify the actual physical force providing the inward resultant.