Verified Solution • 2025–26 Session moderate

Q6.6: NCERT Physics - Part 1 SYSTEMS OF PARTICLES AND ROTATIONAL MOTION 6.6 Solution: Find the components along the x, y, z axes of the angular…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently reverse the order of terms in the cross product expansion, writing $l_x = z p_y - y p_z$ instead of the correct $y p_z - z p_y$. Always verify the cyclic permutation of indices $(x, y, z)$ to ensure the right-hand rule sign convention is preserved.

Find the components along the x, y, z axes of the angular momentum l of a particle, whose position vector is r with components x, y, z and momentum is p with components px, py and pz. Show that if the particle moves only in the x-y plane the angular momentum has only a z-component.

Step-by-Step Verified Solution

**Answer:** lx=ypz−zpyl_x = yp_z - zp_y, ly=zpx−xpzl_y = zp_x - xp_z, lz=xpy−ypxl_z = xp_y - yp_x. If motion is only in x-y plane (z=0z=0, pz=0p_z=0), then lx=ly=0l_x = l_y = 0, so only lzl_z is non-zero. **Step-by-Step Explanation:** The angular momentum is l⃗=r⃗×p⃗\vec{l} = \vec{r} \times \vec{p}:
l⃗=(ypz−zpy)i^+(zpx−xpz)j^+(xpy−ypx)k^\vec{l} = (y p_z - z p_y)\hat{i} + (z p_x - x p_z)\hat{j} + (x p_y - y p_x)\hat{k}
For motion in x-y plane: z=0z = 0, pz=0p_z = 0, so lx=0l_x = 0, ly=0l_y = 0, and lz=xpy−ypxl_z = x p_y - y p_x [citation:31].

All Questions in this Chapter

Q6.1 Q6.2 Q6.3 Q6.4 Q6.5 Q6.6 Q6.7 Q6.8 Q6.9 Q6.10 Q6.11 Q6.12 Q6.13 Q6.14 Q6.15 Q6.16 Q6.17

Related Learning Resources & Exam Preparation

Chapter Practice Bank
Practice all topic-wise questions from SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
Reference Textbook Solutions
Explore complete chapter exercises for NCERT Physics - Part 1
Competitive PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring