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vichka [17]
3 years ago
6

A spinning giant star of initial radius R1 and angular speed ω1 suddenly collapses radially inward reaching a new radius R2 = 0.

5R1 ; its mass remains the same. What is the relation between the kinetic energies of rotation (spin) before and after the collapse? In both cases, approximate the star as a uniform solid sphere.
Mathematics
1 answer:
tiny-mole [99]3 years ago
3 0

Answer:

K1/K2=4

Step-by-step explanation:

The kinetic energy of a rotating sphere is given by:

K=\frac{I*\omega^{2} }{2}

The moment of inertia of a solid sphere is given by

I=\frac{2MR^{2} }{5}

The initial kinetic energy is therefore

K_1=\frac{2MR^{2}*\omega^{2} }{10}

K_1=\frac{MR_1^{2}*\omega^{2} }{5}

The final kinetic energy is given by

K_2=\frac{MR_2^{2}*\omega^{2} }{5}

Therefore the relation K1/K2 if R2 = 0.5R1

\frac{K_1}{K_2} =\frac{5M(R_1)^{2}*\omega^{2} }{5*M(0.5R_1)^{2} \omega^{2}}

The text says nothing about the final angular velocity just the collapse of the collapse of the radius

\frac{K_1}{K_2} =\frac{1 }{(0.5)^{2} }=4

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victus00 [196]

Answer:

Answer:

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San Francisco     4,200   7,200     12,000

Los Angeles       2,400    1,200      3,000

b) Ending Inventory: Matrix D:

                           Hard      Soft      Plastic

San Francisco      400     4,800     3,000

Los Angeles      1,600     7,800     3,000

Step-by-step explanation:

a) Data and Calculations:

Stock on January 1: Matrix A

                              Hard    Soft       Plastic

San Francisco       1,000   3,000    6,000

Los Angeles         1,000   6,000    3,000

Sales in January: Matrix B

                             Hard    Soft       Plastic

San Francisco       700     1,200     2,000

Los Angeles         400       200        500

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Los Angeles      500     500        500

Total Sales over the first 6 months =

Matrix B * 6 = Matrix B6

Sales in January: Matrix B

                             Hard    Soft       Plastic

San Francisco       700     1,200     2,000

Los Angeles         400       200        500

* 6

=

Sales from January to June: Matrix B6

                            Hard    Soft       Plastic

San Francisco     4,200   7,200     12,000

Los Angeles       2,400    1,200      3,000

Matrix C6 = Matrix C * 6

=

Restocking: Matrix C6

                          Hard     Soft       Plastic

San Francisco  3,600   9,000      9,000

Los Angeles    3,000   3,000      3,000

Inventory at the end of June =

Matrix A + Matrix C6 - Matrix B6

= Matrix D

Stock on January 1: Matrix A

                             Hard    Soft       Plastic

San Francisco       1,000   3,000    6,000

Los Angeles         1,000   6,000    3,000

+

Restocking: Matrix C6

                           Hard     Soft       Plastic

San Francisco  3,600   9,000      9,000

Los Angeles    3,000   3,000      3,000

-

Sales from January to June: Matrix B6

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San Francisco     4,200   7,200     12,000

Los Angeles       2,400    1,200      3,000

Ending Inventory: Matrix D:

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San Francisco      400     4,800     3,000

Los Angeles      1,600     7,800     3,000

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