Question

We know the heart shaped object has a moment of inertia of I = 0.5kgm^2. Calculate the change in angular momentum (L) of the object in 5s (~L=~τ∆t). This question deals with angular momentum conservation. Two girls of mass 100 kg each stand at the center of a rotating merry-go-round (MGR) in the shape of a disk of radius 1 m and mass 10 kg. The platform rotates atω= 0.40 rad/s. Let’s call this configuration instant A.

A) Determine the angular momentum of the system (two girls + MGR) at instant A. You will need to find the moment of inertia of the disk and the two girls (point masses).

B) Now the girls start walking radially towards the rim. When one of them has reached the rim, the other is three-quarters of the way there (instant B). Argue that angular momentum is conserved during the process of the girls walking to the rim ( i.e. between instants A and B).

C) Use angular momentum conservation to find the angular velocity of the system at instant B.

D) Calulate the kinetic energy of the system at instant B. The system only has rotational kinetic energy.

10 NA -15 N 37° 90° 6 cm 4 cm 3 4 cm cm 1300 150° 5N 20 N

Answer 1

LON ASN Zo=15x6605 37° - 10x4 100 100 + 2051n30x4 100 90° 3704 6 4cm 86/cm. 4cm SN Oo 7 2N mcw 36° ZON ZAT = (0.72x5) kg-m/ 3.6kg-m/s Instant B Intant A W = 0.4orad's DISK. R=lm m = lokg man mi mi ml=lookg IA = I disk = me 2 = 10x1 kg-m2-5 kg-m2 (L) = IAW = (5x-4) kg-m/s = 2 kg-m/s IB = Idisk + Imi + Imi MR?+ miR²+ mi (38) = 10X + 100 x1 + 100%) 2 (B) 2 2 161.25 kg - m2 Applying angular momentum Conservation 6/W A ZB. IA WA = IB WB DWB= 0.01248ad/s 5x4 = 161-25WB D KEB = I BUB? - 1x 161.25 (0.012432 = 0.01245