Rotational Motion – Stage 1 (Page 7)

Parallel Axis Theorem & Perpendicular Axis Theorem

Often, moment of inertia is required about an axis that does not pass through the center of mass. To handle such cases easily, we use axis theorems.

1. Parallel Axis Theorem

The moment of inertia of a body about any axis is equal to the moment of inertia about a parallel axis passing through the center of mass plus M d².

I = I_cm + M d²

where
I_cm = M.I. about center of mass
M = mass of body
d = distance between axes

2. Conditions for Applying Parallel Axis Theorem

✔ Axes must be parallel
✔ One axis must pass through center of mass
✔ Body must be rigid

3. Example (Very Common in Exams)

Moment of inertia of a rod about one end:

I_end = I_cm + M(L/2)²
= ML²/12 + ML²/4
= ML²/3

4. Perpendicular Axis Theorem

For a planar lamina, the moment of inertia about an axis perpendicular to the plane is equal to the sum of the moments of inertia about two perpendicular axes in the plane.

I_z = I_x + I_y

5. Conditions for Perpendicular Axis Theorem

✔ Applicable only to planar bodies
✔ All three axes must pass through same point
✔ Axes must be mutually perpendicular

6. Why These Theorems Are Powerful

✔ Convert difficult axis problems into easy ones
✔ Avoid lengthy integration
✔ Save time in competitive exams

⚠ Common Student Mistakes

❌ Using perpendicular axis theorem for 3D bodies ❌ Forgetting d² term in parallel axis theorem ❌ Confusing axes directions

IIT-JEE Insight

IIT problems often combine both theorems. Recognizing which theorem applies first is the key skill.

Next: Stage 1 – Page 8
Rotational Kinetic Energy & Work–Energy Theorem

📘 IIT–JEE Physics Mega Library

Complete Intermediate + IIT/JEE Physics Preparation Hub
Concepts • Problems • Exam Mastery • Topper Thinking

🔄 Rotational Motion – Phase 3 (Exam Mastery Series)

Advanced exam-oriented thinking series focusing on traps, execution, pressure handling, and topper strategies.

Phase 3 – Page 1
Phase 3 – Page 2
Phase 3 – Page 3
Phase 3 – Page 4
Phase 3 – Page 5
Phase 3 – Page 6
Phase 3 – Page 7
Phase 3 – Page 8
Phase 3 – Page 9
Phase 3 – Page 10
Phase 3 – Page 11
Phase 3 – Page 12
Phase 3 – Page 13
Phase 3 – Page 14
Phase 3 – Page 15
Phase 3 – Page 16
Phase 3 – Page 17
Phase 3 – Page 18
Phase 3 – Page 19
Phase 3 – Page 21
Phase 3 – Page 22
Phase 3 – Page 23
Phase 3 – Page 24
Phase 3 – Page 25
Phase 3 – Page 26
Phase 3 – Page 27
Phase 3 – Page 28
Phase 3 – Page 29
Phase 3 – Page 30
Phase 3 – Page 31
Phase 3 – Page 32
Phase 3 – Page 33
Phase 3 – Page 34
Phase 3 – Page 35
Phase 3 – Page 36
Phase 3 – Page 37
Phase 3 – Page 38
Phase 3 – Page 39

📚 Complete Physics Libraries

🧠 Advanced Thinking & Core Notes

🌐 Student Learning Channels

This library is designed to convert preparation into rank.
Study systematically • Think like a topper • Execute with confidence

MIND GROW Magazine