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Chapter 1: Q18DQ (page 328)

If two spinning objects have the same angular momentum, do they necessarily have the same rotational kinetic energy? If they have the same rotational kinetic energy, do they necessarily have the same angular momentum? Explain.

Short Answer

Expert verified

No, the objects may not have the same rotational kinetic energy if they have the same angular momentum and vice-versa.

Step by step solution

01

Formulas used

Rotational Kinetic Energy K.E. is

K.E=12濒蝇2=L22l

Where is the moment of inertia,L is angular momentum and蝇 is angular speed.

02

Explanation

According to the formula, we see two objects with the momentum of inertia asl1 andl2 having same angular momentumL does not mean that they have the same rotational kinetic energy.

Similarly, if they have the same rotational kinetic energy, does not mean that they have the same angular momentum L.

03

Conclusion

Hence, the objects may not have the same rotational kinetic energy if they have the same angular momentum and vice-versa.

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