Homework: Angular Momentum Vector And Precession Deadline: 100% until Thursday,

Question

Homework: Angular Momentum Vector And Precession Deadline: 100% until Thursday, April 12 at 11:59 PM Merry Go Round A merry go-round with a a radius of R-1.64 m and moment of inertia 1 -216 kg-m2 is spinning with an tnitial angular speed of ?-1.54 rad/s in the counter clockwise dreection when viewed from above. A per on with mass m-M kg and velocity v-4.7 m/s nns on a path tangent to the merry-go-roud. Oce at the merry-go-round the person jump onand 1) What ts the magnilitude of the initial angular momentum of the merry-go-round kg-m2/s Submit 2) What ts the magnitude of the angular momentum of the person 2 meters before she jumps on the merry go-round 3) What is the magnitude of the angular momentum of the person just before she jumps on to the merry-go-round? kg-ms Submit 4) What is the angular speed of the merry-go-round after the person jumps on? rad/s Submit 5) Once the merry-go-round travels at this new anguiar speed, with what force does the person need to hold on MacBook Pro

Explanation / Answer

1.

Im = moment of inertia of merry-go-round = 216 kgm2

wim = initial angular velocity of merry-go-round = 1.54 rad/s

initial angular momentum is given as

Lim = Im wim = 216 x 1.54 = 332.64

2)

Lip = initial angular momentum of person = m vi R = 58 x 4.7 x 1.64 = 447.064

3)

just before jumping on to the merr-go-round

angular momentum of person = Lip =  447.064

4)

wf = final speed

Using conservation of angular momentum

Lim + Lip = (Im + Ip) wf

Lim + Lip = (Im + m R2) wf

332.64 + 447.064 = (216 + (58) (1.64)2) wf

wf = 2.096 rad/s

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