A uniform disk, a thin hoop, and a uniform sphere, all with the same mass and sa

Question

A uniform disk, a thin hoop, and a uniform sphere, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center. Assume the hoop is connected to the rotation axis by light spokes. With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown. Rank the objects according to their angular momenta after a given time t, least to greatest. greatest. all tie disk, hoop, sphere hoop, disk, sphere hoop, sphere, disk A playground merry-go-round has a radius of 3.0 m and a rotational inertia of 600 kg middot m^2. It is initially spinning at 0.80 rad/s when a 20-kg child crawls from the center to the rim. When the child reaches the rim the angular velocity of the merry-go-round is: 0.62 rad/s 0.73 rad/s 0.80 rad's 0.89 rad/s 1.1 rad/s The angular momentum vector of Earth, due to its daily rotation, is directed: tangent to the equator toward the east tangent to the equator toward the west north south toward the sun A 160-N child sits on a light swing and is pulled back and held with a horizontal force of 100 N. The magnitude of the tension force of each of the two supporting ropes is: 60 N 94 N 120N 190 N 260 N

Explanation / Answer

34.

due to angular momentum conservation

Li = Lf

Ii*wi = If*wf

Ii = 600 kg-m^2

If = Ii + Ichild = Ii + mr^2

If = 600 + 20*3^2 = 780 kg-m^2

wi = 0.80 rad/sec

wf = Ii*wi/If

wf = 600*0.80/780

wf = 0.615 rad/sec = 0.62 rad/sec

Correct option is A.

35.

correct option is C

North

36.

Th = 100 N i

Tv = 160 N j

Tt = 2*T = 100 i + 160 j

2*T = sqrt (Th^2 + Tv^2)

T = [sqrt (160^2 + 100^2)]/2

T = 94.34 N

Correct option is B.

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