Rotational Motion
- A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of… Answer: 1. 1 : 5 Rotational kinetic energy is E=1/2 Iω² , so find each moment of inertia first. Sphere about a diameter: I_s=2/5mR² , so E_s... 1
- A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of 2.0\ rad\ s^-2. Its net acc… Answer: 1. 8.0 Key idea: net acceleration combines tangential and centripetal parts. ω=α t=2×2=4 rad/s. a_t=α r=2×0.5=1 m/s ² ; a_c=ω²r=16×0... 1
- A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first ? Answer: 2. Sphere Key idea: for rolling down an incline, a=gsinθ/1+k²/R² . Smaller k²/R² means larger acceleration and less time. Disk: k²/R... 1
- From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre ? Answer: 2. 13 MR²/32 Key idea: remaining part = full disc minus the cut-out disc, using the parallel axis theorem for the hole. Full disc: I... 1