A ladybug with mass m rides on a disk of mass 7m and radius R. The disk rotates

Question

A ladybug with mass m rides on a disk of mass 7m and radius R. The disk rotates around its central axis at angular speed ?i = 1.5 rad/s. The ladybug crawls in toward the center of the disk. She is now at point r = 0.6R. a) What is the total initial rotational moment? Hint: Ii, total = Idisk + Ii, ladybug. b) What is the total final rotational moment? Hint: If, total = Idisk + If, ladybug. c) What is the total initial angular moment? Hint: Li, total = (Idisk + Ii, ladybug)?i d) What is the final angular speed? Use CoAM: Li, total = Lf, total.

Explanation / Answer

This is a conservation of angular momentum problem. L = Iw L - angular momentum I - moment of inertia w - angular speed You need to look up the moment of inertia for a thin disk of mass m and radius R Id = mR^2/2 The moment of inertia of a point mass at a distance R Ii = mr^2 (a) Initial rotational moment: I1 = Id + Ii plug in the above equations to solve for I (b) Final rotational moment: I2 = Id + li again, this time you use r= 0.6R for the ladybug (c) Initial angular momentum: L1 = (Id + Ii) *w they both have the same speed w=1.5 (d) Final angular speed: We know that angular momentum is conserved so we can write L1=L2 L1 = (I1 + I2)w' w' is the final angular speed. We already solved for L1, I1, I2 in (a) (b) (c) so plug those in to get w'

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