Concept explainers
Three 25-lb rotor disks are attached to a shaft that rotates at 720 rpm. Disk A is attached eccentrically so that its mass center is
Fig. P18.147
Where should 2 lb weights be bolted to disks B and C to balance the system dynamically.
Answer to Problem 18.147RP
The 2 lb weights be bolted to disks B and C to balance the system dynamically are
Explanation of Solution
Given Information:
The weight (W) of the disk is 25 lb.
The shaft rotates at 720 rpm.
The mass center of the disk A is
Calculation:
Draw the free body diagram of the system as shown in Figure (1).
The angular velocity of the shaft is constant. So, the rate of change of angular momentum is zero.
Express the effective force
Here,
Express the effective force
Express the effective force
The sum of the effective forces of the discs should be equal to zero for the system to be in dynamic balance.
Substitute
Substitute
According to principle of impulse momentum, the total momentum is zero.
Express the moment about O:
Here,
Substitute
Substitute
Multiply Equation (1) by
The 2 lb weight is be placed above the shaft for disk C.
Substitute
The 2 lb weight is be placed below the shaft for disk B.
Thus, the 2 lb weights be bolted to disks B and C to balance the system dynamically are
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Chapter 18 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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