A particle of mass m is dropped from rest at t = 0 at the point (-d, 0, 0) and f

Question

A particle of mass m is dropped from rest at t = 0 at the point (-d, 0, 0) and falls vertically in Earth's gravitational field-g 1. (a) What is the expression for the angular momentum of the particle about the origin? (Express your answer in vector form. Use any variable or symbol stated above as necessary.) (b) Calculate the torque on the particle about the origin. (Express your answer in vector form. Use any variable or symbol stated above as necessary.) (c) Is the torque equal to the time rate of change of the angular momentum? Yes O No

Explanation / Answer

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here position vector of the particle is d along -x axis i.e - d i

Velocity of the particle Vt = u - g t j

u =0 ( as it starts from rest)

so vt = - g t j

thus Force on this particle F = -mg j

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angular momentum about origin is obtained from the equation

L = r x mv

L = (- d i) x ( m * (-gt j)

L = mg d t k (k represents along z axis)

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part B :

Torque T = r x F

T = (-di) x (-mg j )

T = m g d K( along z axis)

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part C:

time rate of angular momentum

dL/dt = d(mg d t)/dt

dL/dt = md g k

dL/dt = T from part B

so Yes it is
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