webct8 - I of an L 1. Two identical uniform rods of length...

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I of an L 1. Two identical uniform rods of length l = 2 m, negligible width and mass m = 3 kg are glued to form an L as shown in the figure. Find the moment of inertia of the L for rotations about axis B (perpendicular to the page). The moment of Inertia of a thin rod of mass m and length l about an axis through its center of mass is 2 1 12 ml We can find the moment of inertia of the system about an axis parallel to the symmetry axis of the system and separated from it by a perpendicular distance d,using parallel axis theorem 2 cm I Im d =+ The distance between the axis and the center of mass of the vertical rod is 2 22 5 24 v l dl l  =   . The distance between the axis and the center of mass of the horizontal rod is d h = l /2. Thus, 2 2 2 2 2 () 5 ( ) 12 4 12 4 3(2) 5 3(2) 3(2) (3 ( 2 ) ) ( ) 12 4 12 4 20 kg m system cm v cm h system system system II m d I m d ml ml ml l I I ++ =
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closing door 1. A uniform door of width l = 80 cm, height h = 2.2 m, negligible thickness and mass m = 20 kg is equipped with a self-closing system that pulls on the door with a constant force F = 40 N from a point located at a distance a = 30 cm from the hinges (see figure). The force is perpendicular to the door. Neglect all friction effects. What is the magnitude of the torque about the hinges produced by this force when the door is at an angle θ = 40°, in Nm? sin90 (0.30 m)(40 N)=12 Nm rF a F τ =× = ° = G G The distance between the point of application of the force and the axis (the hinges) is a . The angle between r and the force is 90°. 2. What is the direction of the torque? a. + i b. - i c. + j d. - j e. + k *f. – k Use the right-hand rule on vectors r x F . 3. What is the moment of inertia of the door about its hinges? The moment of inertia of the door about its hinges is the same as the moment of inertia of a rod about one of its ends (how tall the door is does not make any difference). Thus, r F r
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22 2 11 (20 kg)(0.8 m) 4.2 kg m 33 IM L == = 4. Find the magnitude of the angular acceleration of the door.
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This homework help was uploaded on 03/26/2008 for the course PHYS 221 taught by Professor Herrera-siklody during the Spring '08 term at Iowa State.

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webct8 - I of an L 1. Two identical uniform rods of length...

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