with units please Do all work on this page (front and /or back) Relative point v

Question

with units please

Do all work on this page (front and /or back) Relative point value are indicated . partial credit will be given when earned by legible relevant work , but any credit may be lost due to accompanying incorrect steps. Unit are part of any correct physical quantity. Use the following values if needed: 1 foot= 0.30 meter 1hp= 746 watt(w) g=9.8 m/s2 G=6.67 times 10-11 N m2/kg2 Some moments of inertia (if uniform, about center); disk (1/2)MR2 sphere (2/5)MR2 pierre, an on -ice entertainer, is spinning at 10 rad/s on smooth ice with a moment of inertia of 12 kg m2 , of which at present a negligible part is due to two 7.5-kg gloves on his hands. If he swing his arms out to give the gloves a diameter of 1.6 m, what will be his new rotation rate? A fancy wheel (outside diameter 0.40 m, mass 10 kg) is mounted on a fixed horizontal frictionless axle A massless string is tied to it and wrapped around its rim; you are pulling the end of the string eastward causing a torque of 4.8 N m, thus giving the wheel an angular acceleration of 16 rad/s2 which has continued for 0.25 s. What is the moment of inertia of the wheel? What is the net force by the axle on the wheel now ?

Explanation / Answer

1)

Conservation of angular momentum:

I1 w1 = I2 w2

==> I2 = I1 + 2 (m L^2) = 12 + 2 * (7.5*(1.6/2)^2) = 21.6 Kg.m2

==> I1 w1 = I2 w2

==> w2 = (I1/I2) w1 = (12/21.6) *10 = 5.56 rad/s

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2)

a)

I = 0.5 M R^2 = 0.5 * 10 * 0.2 * 0.2 = 0.2 Kg.m2

b)

torque = I alpha

F R = I alpha

==> F = I alpha/R = 0.2*16/0.2 = 16 N

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