Concept explainers
Two friction disks A and B are brought into contact when the angular velocity of disk A is 240 rpm counterclockwise and disk B is at rest. A period of slipping follows and disk B makes two revolutions before reaching its final angular velocity. Assuming that the angular acceleration of each disk is constant and inversely proportional to the cube of its radius, determine (a) the angular acceleration of each disk, (b) the time during which the disks slip.
Fig. P15.34 and P15.35
(a)
Find the angular acceleration of disk A and B.
Answer to Problem 15.35P
The angular acceleration of disk A and B are
Explanation of Solution
Given information:
Consider the initial and final angular velocity of disk A are as follows:
Consider the initial and final angular velocity of disk B are
Consider the angular acceleration of the disk A and B are denoted by
Consider the angular displacement of the disk B is denoted by
Show the value of the angular displacement
The angular acceleration of disk A and B are constant.
The radius of the disk A and B are
The angular acceleration of disk A and B are inversely proportional to cube of their radius.
Calculation:
Calculate the final angular velocity of disk A using the relation:
Substitute
Calculate the angular displacement of the disk B using the relation:
Modify above Equation using Equation (1).
Substitute 0 for
Calculate the final angular velocity of the disk B using the relation:
Modify above Equation using Equation (1).
Substitute 0 for
Consider the contact point between the disk A and B are denoted by C.
Calculate the velocity at point C using the relation:
Substitute
Calculate the velocity at point C using the relation:
Substitute
Equate Equation (3) and (4).
Divide Equation (1) by (5).
Calculate the angular acceleration of disk A as follows:
Substitute
Thus, the angular acceleration of the disk A is
Calculate the angular acceleration of disk B as follows:
Substitute
Thus, the angular acceleration of the disk B is
(b)
Find the time at which the disk slip.
Answer to Problem 15.35P
The disk slip at time
Explanation of Solution
Given information:
Calculation:
Refer to Part (a).
Refer Equation (6).
The time at which the disk slip is at
Thus, the time at which the disk slip is at
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Chapter 15 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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