Key relationship
a = gsinθ/(1+β); v=at; ω=v/r; β=I/(Mr²).
Physics · Class 11
Roll a ring, cylinder or sphere
Gravitational energy becomes both translational and rotational kinetic energy. Bodies with a smaller shape factor need less rotational energy per unit speed and accelerate faster. The no-slip condition is v=ωr.
Open the interactive experiment →Roll a ring, cylinder or sphere
சறுக்காமல் உருளும்போது v = ωr. நிலைமத் திருப்புத்திறன் குறைவான வடிவம் சரிவில் வேகமாக முடுக்கம் பெறும்.
Key notes, relationships and model limits
Remember
Gravitational energy becomes both translational and rotational kinetic energy. Bodies with a smaller shape factor need less rotational energy per unit speed and accelerate faster. The no-slip condition is v=ωr.
Common trap
Static friction in ideal rolling does no work at the stationary contact point.
Model limits
Rigid bodies start from rest and roll without slipping down an ideal slope. Static friction is sufficient; no rolling resistance. The horizontal axis is simulation time.
What you will learn
Link rolling kinematics, shape-dependent inertia and energy partition.
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
At 20°, sphere a=9.81sin20°/1.4=2.40 m/s², cylinder a=2.24 m/s² and ring a=1.68 m/s².
Why this matters
The model connects roll a ring, cylinder or sphere with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
Which reaches a given distance first on this ideal slope?
- The thin ring
- The solid sphere
- The solid cylinder
Read the explanation
The shape factors are sphere 0.4, cylinder 0.5, ring 1; acceleration decreases as β increases.
Course connection: Class XI Chapter 6. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.