The following information pertains to the next two questions. A light rod of len

Question

The following information pertains to the next two questions. A light rod of length 2L has 2 small heavy masses (each with mass m) attached at the end and the middle, and the rod is attached to an axis of rotation that is perpendicular to the plane of the page. A second light rod of length L has a small heavy mass 4m attached to the same axis of rotation, as shown. All the rods are horizontal. The acceleration due to gravity points vertically downwards (toward the bottom of the page).

1) What is the rotational inertia of the system about the axis? Show all work.

A) 2mL2

B) 4mL2

C) 6mL2

D) 8mL2

E) None of these

2) What is the magnitude of the net torque due to gravity about the axis? Show all work.

A) mgL

B) 2mgL

C) 3mgL

D) 4mgL

E) 5mgL

Explanation / Answer

Here

1) as the moment of inertia of a mass is given as

I = m * R^2

for the total moment of inertia about the axis

I = 4m * L^2 + m * L^2 + m * (2L)^2

I = 8 mL^2

the rotational inertia of the system about the axis is 8 mL^2

2)

for net torque due to gravity = 4 *m * g * L - m * g * L -2m * g *L

net torque due to gravity = m * g *L

the net torque due to gravity is A) mgL

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