Comparison of linear and rotational motion
- The angular speed of a fly wheel moving with uniform angular acceleration changes from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration in rad/s^2 is : Answer: 3. 4π Convert rpm to rad/s using ω=2π N/60 . Δ N=3120-1200=1920 rpm, so Δω=2π×1920/60=64π\ rad/s . α=Δω/t=64π/16=4π\ rad/s² . Option... 1
- A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it ? Answer: 1. 3 J To stop the disc we must remove its total kinetic energy, which is translational plus rotational. K=1/2mv²+1/2Iω² with I=1/2m... 1
- A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (K_t) as well as rotational kinetic energy (K_r) simultaneously. The ratio K_t:(K_t+K_r) for the sphere is Answer: 3. 5 : 7 For a solid sphere rolling without slipping, K_t=1/2mv² and K_r=1/2Iω²=1/2·2/5mR²·v²/R²=1/5mv² . K_t/K_t+K_r=1/2/1/2+1/5=5/... 1
- Two rotating bodies A and B of masses m and 2m with moments of inertia I_A and I_B (I_B>I_A) have equal kinetic energy of rotation. If L_A and L_B be their angular momenta respectively, then Answer: 2. L_B>L_A Express angular momentum through kinetic energy: K=L²/2I , so L=√(2IK) . The kinetic energies are equal, so L∝sqrt I . Si... 1