Key relationship
L = I₀ω₀ = Iω; I = 2mr²; K = L²/(2I).
Physics · Class 11
Pull rotating masses inward
With no external torque, angular momentum remains constant. Bringing mass closer to the rotation axis reduces inertia and increases angular speed. The pulling mechanism supplies the extra kinetic energy.
Open the interactive experiment →Pull rotating masses inward
வெளிப்புற திருப்புவிசை இல்லாவிட்டால் கோண உந்தம் மாறாது. நிறைகளை அச்சுக்கு அருகே கொண்டுவரும்போது கோண வேகம் அதிகரிக்கும்.
Key notes, relationships and model limits
Remember
With no external torque, angular momentum remains constant. Bringing mass closer to the rotation axis reduces inertia and increases angular speed. The pulling mechanism supplies the extra kinetic energy.
Common trap
Angular-momentum conservation does not imply kinetic-energy conservation.
Model limits
Two identical point masses on a massless rotating support, moved quasistatically without external torque. Pulling can do work, so rotational kinetic energy need not be constant.
What you will learn
Conserve angular momentum and account for work during changing inertia.
Try the experiment
Try both scenarios, change one control, and predict the result before checking the graph and readouts.
Think of it this way
Change one input while keeping the others fixed, as you would in a controlled experiment.
Worked example
Two 1 kg masses at 1 m with ω₀=2 rad/s have L=4 kg·m²/s. At 0.5 m, I=0.5 kg·m² and ω=8 rad/s.
Why this matters
The model connects pull rotating masses inward with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
If both radii halve, how does angular speed change?
- It becomes twice as large
- It becomes four times as large
- It becomes half as large
Read the explanation
I is proportional to r², so halving r divides I by four; conserved Iω multiplies ω by four.
Course connection: Class XI Chapter 6. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.