Physics · The moment of inertia, the radius of gyration, values of moments of inertia for simple geometrical objects
An object is allowed to roll down an inclined plane starting from rest (consider
An object is allowed to roll down an inclined plane starting from rest (consider the object to be uniform and having same mass) then object having largest rotational momentum is (if rotated with same angular momentum)
- A. solid sphere
- B. spherical shell
- C. solid disc
- D. thin hollow cylinder
Step-by-step solution
For rolling objects down an incline starting from rest, the angular momentum L at the bottom is proportional to k/√(1+k) where k = I/(mR^2). Among the given shapes, k values: solid sphere 0.4, disc 0.5, spherical shell 2/3≈0.667, thin hollow cylinder 1. The factor k/√(1+k) is largest for the hollow cylinder (≈0.707), giving it the largest rotational momentum.
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