The L-shaped object in the figure(Figure 1) consists of three masses connected b

Question

The L-shaped object in the figure(Figure 1) consists of three masses connected by light rods. Figure 1:

A) Find the WORK that must be done on this object to accelerate it from rest to an angular speed of 2.50 about the x axis. Express your answer using two significant figures.

B) About the y axis. Express your answer using two significant figures.

C) About the z axis (which is through the origin and perpendicular to the plane of the figure). Express your answer using two significant figures.

Thanks in advance to anyone who can help!

Explanation / Answer

sol: the moment of inertia of the whole system rotating in the x-axis, only concerns the 9 kg mass: Ix = (9 kg)(1 m)^2 = 9 kg*m^2 And Iy only concerns the 2.5 kg mass: Iy = (2.5 kg)(2 m)^2 = 10 kg*m^2 Then obviously Iz is the sum of Ix and Iy, 19 kg*m^2. You will use those different I's and the desired angular acceleration, a, to find the torque needed, t, using the rotational version of Newton's Second Law: t = I*a Easy enough: tx = (9 kg*m^2)(1.2 s^-2) = 10.8 N*m ty = (10 kg*m^2)(1.2 s^-2) = 12.0 N*m tz = (19 kg*m^2)(1.2 s^-2) = 22.8 N*m

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