Concept explainers
(a)
To Calculate:The maximum value of angular speed of sun and the time period corresponding to the maximum angular speed of the sun.
(a)
Answer to Problem 21P
The maximum value of angular speed of sun is
The time period corresponding to the maximum angular speed of the sun is
Explanation of Solution
Given data:
Universal gravitational constant,
Radius of the sun,
Measured
Moment of inertia for a sphere about axis through its center,
Time period of sun is
Formula used:
The gravitational attraction force on mass
The centripetal force on the mass
Here
Calculation:
The above two forces are equal in magnitude, but to estimate maximum angular speed, we must use inequality as below:
The maximum value of angular speed of sun is
The time period corresponding to the maximum angular speed of the sun is
Conclusion:
The maximum value of angular speed of sun is
The time period corresponding to the maximum angular speed of the sun is
(b)
To Calculate:
The angular momentum of the Jupiter
The angular momentum of the Saturn
To Compare: The calculated angular momentum value of Jupiter and Saturn with that of measured value of angular momentum of Sun.
(b)
Answer to Problem 21P
The angular momentum of the jupiter is
The angular momentum of Saturn is
Explanation of Solution
Given data:
Mean distance of the Jupiter is
Mean distance of the Saturn is
Orbital time period of Jupiter is
Orbital time period of Saturn is
Formula Used:
Angular momentum of the Jupiter,
Here, the linear velocity of the Jupiter,
Calculation:
The angular momentum of the Jupiter is
By substituting all known numerical values in the equation
Similarly, the angular momentum of the Saturn is
Consider the ratio,
Conclusion:
The angular momentum of the jupiter is
The angular momentum of Saturn is
The ratio is 0.00703.
(c)
To Calculate:The sun new rotational speed. Ratio of the time period of sun with the result in part (a).
(c)
Answer to Problem 21P
The sun new rotational speed is
The ratio of time period of sun with the result in part (a) is
Explanation of Solution
Given data:
Mean distance of the Jupiter is
Mean distance of the Saturn is
Time period of sun is
Formula Used:
The gravitational attraction force on mass
The
Here,
Calculation:
The final angular momentum of sun is
Substitute all known numerical values in the equation
The sun new rotational speed is:
The corresponding time period of the sun is
By comparing this time period of Sun with result in part
Conclusion:
The sun new rotational speed is
The ratio of time period of sun with the result in part (a) is
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Chapter 11 Solutions
Physics For Scientists And Engineers Student Solutions Manual, Vol. 1
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