Explanation Given information: The inner radius ( r ) of the platform-rim A is 200 mm . The mass ( m A ) of the platform-rim A is 5 kg. The radius of gyration ( k ) of the platform-rim A is 175 mm. The angular velocity of the platform A is 50 rpm. The mass ( m B ) of the disk B is 3 kg. The radius ( r B ) of the disk B is 80 mm. Calculation: Find the moment of inertia of platform A using the equation: I ¯ A = m A k 2 Substitute 5 kg for m A and 175 mm for k . I ¯ A = ( 5 ) ( 175 mm × 1 m 1 , 000 mm ) 2 = 0.153125 kg ⋅ m 2 Find the moment of inertia of disk B using the equation: I ¯ B = 1 2 m B r B 2 Substitute 3 kg for m B and 80 mm for r B . I ¯ B = 1 2 ( 3 ) ( 80 mm × 1 m 1 , 000 mm ) 2 = 9.6 × 10 − 3 kg ⋅ m 2 Consider at position 1, the disk B is at rest. Sketch the impulse and momentum diagram at position 1 as shown in Figure (1). Consider at position 2, the disk B moves with platform A . Sketch the impulse and momentum diagram at position 2 as shown in Figure (2). Refer Figure (2), Find the distance between center of platform to center of disk in position 2. r A B = 200 − 80 = 120 mm × 1 m 1 , 000 mm = 0.12 m Find the equation of velocity ( v B ) of disk B using kinematics: v B = r A B ω 2 Substitute 0

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Author: BEER

Publisher: MCG

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Chapter 17.2, Problem 17.86P

To determine

The final angular velocity of the platform.

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Chapter 17.2, Problem 17.85P

Chapter 17.2, Problem 17.87P

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Chapter 17 Solutions

VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS

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