
Concept explainers
Solve Prob. 16.35, assuming that the couple M is applied to disk A.

i.
The angular acceleration of gear A.
Answer to Problem 16.36P
Angular acceleration of gear A = 6.057 rad/s2
Explanation of Solution
Given:
Mass of Gear A,ma = 9 kg
radius of gyration of gear A,
Mass of gear B, mb = 9 kg
radius of gyration of gear B,
Mass of Gear C,mc = 3 kg
radius of gyration of gear C,
Magnitude of Couple applied on gear A, M = 5N-m
Concept used:
Mass moment of acceleration is given by-
The tangential force acting on a gear will provide the angular acceleration to the gear. Therefore,
The free body diagram of the three gears is as following-
Calculation:
The tangential component of two gears in mesh will be equal, therefore,
Since,
For gear B,
Since, gear a A and B are of same size, therefore because of symmetry, gear C will exert same force on gear B as on gear A.
For gear C,
For gear A,
Angular acceleration of gear A,
Conclusion:
Angular acceleration of gear A = 6.057 rad/s2

ii.
The tangential force that gear A exerts on gear C.
Answer to Problem 16.36P
Force exerted by gear C on gear A = 11.278 N
Explanation of Solution
Given:
Mass of Gear A,ma = 9 kg
radius of gyration of gear A,
mass of gear B, mb = 9 kg
radius of gyration of gear B,
mass of Gear C,mc = 3 kg
radius of gyration of gear C,
Magnitude of Couple applied on gear A, M = 5N-m
Concept used:
Mass moment of acceleration is given by-
The tangential force acting on a gear will provide the angular acceleration to the gear. Therefore,
The free body diagram of the three gears is as following-
Calculation:
Angular acceleration of gear A = 6.057 rad/s2
The tangential component of two gears in mesh will be equal, therefore,
Since,
For gear B,
Since gear a A and B are of same size, therefore because of symmetry, gear C will exert same force on gear B as on gear A.
For gear C,
Angular acceleration of gear A,
Tangential force on gear A, on gearC-
Conclusion:
Force exerted by gear C on gear A = 11.278 N
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Chapter 16 Solutions
Vector Mechanics For Engineers
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