Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0.1 kg–m² and 10 rads⁻¹ respectively while those for the second one are 0.2 kg–m² and 5 rads⁻¹ respectively. At some instant, they get stuck together and start rotating as a single system about their common axis with some angular speed. The kinetic energy of the combined system is:
Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0.1 kg–m² and 10 rads⁻¹ respectively while those for the second one are 0.2 kg–m² and 5 rads⁻¹ respectively. At some instant, they get stuck together and start rotating as a single system about their common axis with some angular speed. The kinetic energy of the combined system is:
By conservation of angular momentum, I? ω? + I? ω? = (I? +I? )ω
ω = (I? ω? +I? ω? )/ (I? +I? ) = (0.110 + 0.25)/ (0.1+0.2) = 2/0.3 = 20/3 rad/s
K = ½ (I? +I? )ω² = ½ (0.3) (20/3)² = 20/3 J.
Upvote 
Taking an Exam? Selecting a College?
Get authentic answers from experts, students and alumni that you won't find anywhere else.
On Shiksha, get access to
Learn more about...
Physics Ray Optics and Optical Instruments 2021
View Exam DetailsMost viewed information
SummaryDidn't find the answer you were looking for?
Search from Shiksha's 1 lakh+ Topics
Ask Current Students, Alumni & our Experts
Have a question related to your career & education?
See what others like you are asking & answering