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Question

https://d2vlcm61l7u1fs.cloudfront.net/media/486/486be8e4-80c0-4c9a-b7ce-6ce43b4b6bfc/phpaehs1h.png The drawing shows two identical systems of objects; each consists of the same three small balls connected by massless rods. In both systems the axis is perpendicular to the page, but it is located at a different place, as shown. The same force of magnitude F is applied to the same ball in each system (see the drawing). The masses of the balls are m1 = 9.2 kg, m2 = 6.4 kg, and m3 = 7.7 kg. The magnitude of the force is F = 426 N. (a) For each of the two systems, determine the moment of inertia about the given axis of rotation. (b) Calculate the torque (magnitude and direction) acting on each system. (c) Both systems start from rest, and the direction of the force moves with the system and always points along the 4.00-m rod. What is the angular velocity of each system after 5.02 s?

Explanation / Answer

Given the masses,

a) For System A: I = 9.2kg * (0m)² + 6.4kg * (3m)² + 7.7kg * (5m)² = 250.1 kg·m²
    For System B: I = 9.2kg * (5m)² + 6.4kg * (4m)² + 7.7kg * (0m)² = 332.4 kg·m²

b) System A: = F x r = 426N x 3m = 1278 N·m cw
B:System B: = 426N x 0 = 0 N·m

c) Sysyem A: = 1278 N·m = I = 250.1 kg·m² *
= 5.1 rad/s²
= t = 5.1 rad/s² * 5.02s = 25.6 rad/s

B: System B ; = 0

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