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Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Dish B has an initial angular velocity w0 when it is brought into contact with disk A, which is at rest. Show that the final angular velocity of disk B depends only on W0 and the ratio of the masses mA and mB of the two disks.

Expert Solution

Step 1

Given:

The initial angular velocity of disk B is ω₀.
The mass of the disk A is m_A.
The mass of the disk B is m_B.
The radius of disk A and B are r_A and r_B

Let the final angular velocity at disk A and B be ω_A and ω_B and assume a point C between A and B.

Due to zero slippage, the velocity at point C is

$v_{c} = r_{A} ω_{A} = r_{B} ω_{B}$

The expression of moment of inertia for disk A and B is,

$I_{A} = \frac{1}{2} m_{A} r_{A}^{2} I_{B} = \frac{1}{2} m_{B} r_{B}^{2}$

Here I_A and I_B are the moment of inertia due to A and B.

The first moment about disk A is zero as it’s at rest.

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