Concept explainers
Disk B is at rest when it is brought into contact with disk A, which has an initial angular velocity
i.
Angular velocities have are independent of
Answer to Problem 16.44P
Hence proved, the final angular velocities have are independent of
Explanation of Solution
Given:
Disk A, of mass ma radius of disk A, rA
Initial Angular velocity of disk B =
mass of disk B, mB
radius of disk B, rB
Coefficient of kinetic friction =
Concept used:
When the two disks come in contact, a friction force between them comes into play and it causes the disk A to start rotating while accelerating with a certain angular acceleration in anti-clockwise direction. The reaction of the friction force on disk A will be acting on disk B, such that while it will still be rotating in clockwise direction, but with a certain. angular deacceleration. This will continue till the tangential velocity of both the disks become equal. At that point,
While accelerating from rest for disk A,
While deaccelerating from an angular velocity
Therefore, condition of velocity equivalence is
Further, Mass moment of inertia for a disk is given by-
The tangential force acting on a disk will provide the angular acceleration to the disk. Therefore,
Mass moment of inertia of disk A =
Mass moment of inertia of disk B =
Friction force between two disks, F =
For disk B,
From eq (2)
For disk A,
From eq(2)
Disk A will continue to deaccelerate, and disk B will continue to accelerate till their tangential acceleration becomes equal.
from eq (1)
From equation (3) and (4), we see that the final angular velocities of the two disks are independent of
Conclusion:
Hence proved, the final angular velocities have are independent of
ii.
Angular velocities in terms of in terms od
Answer to Problem 16.44P
Angular velocity of disk is expressed as
Explanation of Solution
Given:
Disk A, of mass ma radius of disk A, rA
Initial Angular velocity of disk B =
mass of disk B, mB
radius of disk B, rB
Coefficient of kinetic friction =
Concept used:
When the two disks come in contact, a friction force between them comes into play and it causes the disk A to start rotating while accelerating with a certain angular acceleration in anti-clockwise direction. The reaction of the friction force on disk A will be acting on disk B, such that while it will still be rotating in clockwise direction, but with a certain. angular deacceleration. This will continue till the tangential velocity of both the disks become equal. At that point,
While accelerating from rest for disk A,
While deaccelerating from an angular velocity
Therefore, condition of velocity equivalence is
Further, Mass moment of inertia for a disk is given by-
The tangential force acting on a disk will provide the angular acceleration to the disk. Therefore,
Mass moment of inertia of disk A =
Mass moment of inertia of disk B =
Friction force between two disks, F =
For disk B,
From eq (2)
For disk A,
From eq(2)
Disk A will continue to deaccelerate, and disk B will continue to accelerate till their tangential acceleration becomes equal.
from eq (1)
Conclusion:
Angular velocity of disk i
Is expressed as
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Chapter 16 Solutions
Vector Mechanics For Engineers
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