Explanation Given information: Mass of the gear A (m A ) = 1kg. Radius of gyration of the gear A (k A ) = 30mm. Mass of the gear B (m B ) = 4kg. Radius of gyration of the gear B (k B ) = 75mm. Mass of the gear C (m C ) = 9kg. Radius of gyration of the gear C (k C ) = 100mm. Angular velocity of gear A (N A ) = 300rpm Radius of gear A (r A ) = 50mm Radius of gear B (r B ) = 100mm Radius of gear C (r C ) = 150mm Calculation: Initial kinetic energy is zero because gear is in rest i.e. initial angular velocity is zero E 1 =0 Moment of inertia of gear A I A = m A k A 2 I A = 1 × 0.030 2 I A = 0.0009 k g − m 2 Moment of inertia of gear B I B = m B k B 2 I B = 4 × 0.075 2 I B = 0.0225 k g − m 2 Moment of inertia of gear C I C = m C k C 2 I C = 9 × 0.100 2 I C = 0.09 k g − m 2 Angular velocity of the gear A, ω A = 2 π N A 60 ω A = 2 π × 300 60 ω A = 31.4 r a d i a n / s Gear A mess with Gear B. So angular velocity ration is given as ω B ω A = r A r B ω B ω A = 50 100 ω B = 0.5 × ω A ω B = 0.5 × 31.4 ω B = 15.7 r a d i a n / s Gear C mess with compound gear B ω B ω C = r C r 1 ω B ω C = 150 50 ω C = 1 3 × ω B ω C = 1 3 × 15

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ISBN: 9781260265521

Author: BEER

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Chapter 17.1, Problem 17.15P

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Number of revolutions by the disk A.

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Chapter 17 Solutions

VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS

Ch. 17.1 - A round object of mass m and radius r is released...Ch. 17.1 - Prob. 17.CQ2P Ch. 17.1 - Prob. 17.CQ3P Ch. 17.1 - Prob. 17.CQ4P Ch. 17.1 - Slender bar A is rigidly connected to a massless...Ch. 17.1 - A 200-kg flywheel is at rest when a constant 300 N...Ch. 17.1 - The rotor of an electric motor has an angular...Ch. 17.1 - Two uniform disks of the same material are...Ch. 17.1 - Two disks of the same material are attached to a...Ch. 17.1 - Prob. 17.5P

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Number of revolutions by the disk A.

Solution Summary: The author calculates the moment of inertia of gear A, which is zero because gear is in rest.

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Number of revolutions by the disk A.

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