The L-shaped object in the figure below consists of three masses (m1 = 9.00 kg,

Question

The L-shaped object in the figure below consists of three masses (m1 = 9.00 kg, m2 = 1.38 kg and m3 = 2.42 kg) connected by light rods of length L1 = 1.40 m and L2 = 2.06 m. What torque must be applied to this object to give it an angular acceleration of 1.27 rad/s2 if it is rotated about the axis? What torque must be applied to this object to give it an angular acceleration of 1.27 rad/s2 if it is rotated about the axis? What torque must be applied to this object to give it an angular acceleration of 1.27 rad/s2 if it is rotated about the axis (which is through the origin and perpendicular to the page)?

Explanation / Answer

example What torque must be applied? Have no idea!? The L-shaped object consists of three masses (m1 = 8.84 kg, m2 = 1.32 kg and m3 = 2.51 kg) connected by light rods of length L1 = 1.26 m and L2 = 1.94 m. What torque must be applied to this object to give it an angular acceleration of 1.20 rad/s2 if it is rotated about the axis? What torque must be applied to this object to give it an angular acceleration of 1.20 rad/s2 if it is rotated about the axis? What torque must be applied to this object to give it an angular acceleration of 1.20 rad/s2 if it is rotated about the axis (which is through the origin and perpendicular to the page)? M2 is at the origin, M1 is on the y axis, and M3 is on the x axis. I have no idea what to do. Can someone please help me? ans The moment of inertia about some axis is given by: I = m1(r1)^2 + m2(r2)^2 + m3(r3)^2 where r1, r2, and r3 are the distances from the axis to m1, m2, and m3 respectively. Also, torque = (moment of inertia)(angular acceleration). Rotating about the x-axis: Since m2 and m3 are on the x-axis, r2 = r3 = 0, and r1 = L1. So: I = m1(L1)^2 = (8.84 kg)(1.26 m)^2 = 14.03kg*m^2 and T = Ia = (14.03kg*m^2)(1.20 rad/s^2) = 16.84 Nm Rotating about the y-axis: Since m1 and m2 are on the x-axis, r1 = r2 = 0, and r3 = L2. So: I = m3(L2)^2 = (2.51 kg)(1.94 m)^2 = 9.45 kg*m^2 and T = Ia = ( 9.45 kg*m^2)(1.20 rad/s^2) = 11.37 Nm Rotating about the z-axis (which is through the origin and perpendicular to the page): Since m2 is on the x-axis, r2 = 0, r1 = L1, and r3 = L2. So: I = m1(L1)^2 + m3(L2)^2 = (8.84 kg)(1.26 m)^2 + (2.51 kg)(1.94 m)^2 = 23.48 kg*m^2 and T = Ia = (23.48 kg*m^2)(1.20 rad/s^2) = 28.18 Nm

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