3. The four objects in the figures shown are moving as indicated by the arrows.

Question

3. The four objects in the figures shown are moving as indicated by the arrows. A curved arrow indicates rotation about the center. For object A, use the coordinates shown. For the others, take the origin to be at the center of the circle. R Y ?L-29 earth hoop disk mass on a string For each, find a. the total linear momentum of the system b. the total angular momentum of the system c. the total energy of motion Express your answers in terms of m, v, and R. Rank the systems, from largest to smallest, for each of the variables you calculated in parts (a) through (c). d.

Explanation / Answer

3. a. linear momentum of the system

A. linear momentum = -mv j ( where i and j are unit vectors along x and y directions respectively)

B. linear momentum = 0 ( as the object has no linear velocity in the given frame of reference)

C. linear momentum = 0 ( as the object has no linear velocity in the given frame of reference)

D. linear momentum = 0 ( as the object has no linear velocity in the given frame of reference)

b. total angular momentum of the system

A. L = -mv*2R k ( where k is unit vector along z axis)

B. L = I*w k

now, I for hoop = mR^2

hence

L = mR^2*v/R = mvR k

C. L = Iw k

I = 0.5mR^2

hence

L = 0.5 mvR k

D. mass on a string

L = Iw k

I = mR^2

hence

L = mRv k

c. total energy of motion

A. E = 0.5mv^2 - mgh ( where h is the height ofthe object)

B. E = 0.5*Iw^2 = 0.5*mR^2*v^2/R^2 = 0.5mv^2

C. E = 0.5*I*w^2 = 0.25mv^2

D. E = 0.5mv^2

d. ranking systems from largest to smallest

A. in terms of linear momentum, B = C = D > A

B. angular momentum, B = D > C > A

C. total energy, B = D > C > A

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