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Rotational Mechanics

Rotational Mechanics

by Anshul Chanchlani -
Number of replies: 2

A turn table of mass M and radius R is rotating with angular velocity omega knot on frictionless bearing. A spider of mass m falls vertically onto the rim of the turn table and then walks in slowly towards the centre of the table. What is the angular velocity of the system when spider is at a distance r from the centre. Compute also the angular velcoity of the turn table when the spider is at the rim . Is the energy of the system in this problem conserved?

Ans : omega =  omega knot / ( 1 + (2mr^2/MR^2))

        omega (rim) = omega knot  M/ M+2m)

       Energy not conserved

Please reply with explanation..

In reply to Anshul Chanchlani

Re: Rotational Mechanics

by Manish Verma -

When the spider collides and when it crawls, the forces normal reaction and friction* are internal forces if we consider the turn table + spider as a system.

Applying COAM between the very first (before collision) and the very last (distance r from the centre) points.

\(I\omega_0 = I"\omega"\)

\(\frac {MR^2}{2}\omega_0=(\frac{MR^2}{2}+mr^2)\omega"\)

\(\omega"\) can be obtained.

Now, you should try the other parts. If you face problems with those, you can send me a private message in the virtual classoom and I can schedule a short online live session for you for this.

*Friction between turn table and spider is required during crawling.