13. Rotational Inertia & Energy

Intro to Rotational Kinetic Energy

Rotational Kinetic Energy

A flywheel is a rotating disc used to store energy. What is the maximum energy you can store on a flywheel built as a solid disc with mass 8 × 104 kg and diameter 5.0 m, if it can spin at a max of 120 RPM?

What is the mass of a solid sphere with radius <math display="inline"><mrow><mn>5.0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow></math>, that has <math display="inline"><mrow><mn>2.5</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">J</mi></mrow></math> of kinetic energy when it rotates at <math display="inline"><mrow><mn>34</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">rad</mi><mo>/</mo><mi mathvariant="normal" class="MathML-Unit">s</mi></mrow></math>?

A uniform sphere with mass 28.0 kg and radius 0.380 m is rotating at constant angular velocity about a stationary axis that lies along a diameter of the sphere. If the kinetic energy of the sphere is 236 J, what is the tangential velocity of a point on the rim of the sphere?

Mass of re-designed flywheel

A wheel is turning about an axis through its center with constant angular acceleration. Starting from rest, at t = 0, the wheel turns through 8.20 revolutions in 12.0 s. At t = 12.0 s the kinetic energy of the wheel is 36.0 J. For an axis through its center, what is the moment of inertia of the wheel?

Anderson Video - Race Down Incline

When solid sphere 4 m in diameter spins around its central axis at 120 RPM, it has 10,000 J in kinetic energy. Calculate the sphere’s mass.

An airplane propeller is 2.08 m in length (from tip to tip) with mass 117 kg and is rotating at 2400 rpm (rev/min) about an axis through its center. You can model the propeller as a slender rod. (a) What is its rotational kinetic energy? (b) Suppose that, due to weight constraints, you had to reduce the propeller’s mass to 75.0% of its original mass, but you still needed to keep the same size and kinetic energy. What would its angular speed have to be, in rpm?

The flywheel of a gasoline engine is required to give up 500 J of kinetic energy while its angular velocity decreases from 650 rev/min to 520 rev/min. What moment of inertia is required?

If we multiply all the design dimensions of an object by a scaling factor f, its volume and mass will be multiplied by f^3. (b) If a 1/48 scale model has a rotational kinetic energy of 2.5 J, what will be the kinetic energy for the full-scale object of the same material rotating at the same angular velocity?

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1. Intro to Physics Units

2. 1D Motion / Kinematics

3. Vectors

4. 2D Kinematics

5. Projectile Motion

6. Intro to Forces (Dynamics)

7. Friction, Inclines, Systems

8. Centripetal Forces & Gravitation

9. Work & Energy

10. Conservation of Energy

11. Momentum & Impulse

12. Rotational Kinematics

14. Torque & Rotational Dynamics

15. Rotational Equilibrium

16. Angular Momentum

17. Periodic Motion

18. Waves & Sound

19. Fluid Mechanics

20. Heat and Temperature

21. Kinetic Theory of Ideal Gases

22. The First Law of Thermodynamics

23. The Second Law of Thermodynamics

24. Electric Force & Field; Gauss' Law

25. Electric Potential

26. Capacitors & Dielectrics

27. Resistors & DC Circuits

28. Magnetic Fields and Forces

29. Sources of Magnetic Field

30. Induction and Inductance

31. Alternating Current

32. Electromagnetic Waves

33. Geometric Optics

34. Wave Optics

36. Special Relativity

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Rotational Dynamics of Rolling Motion

Types of Motion & Energy

Torque with Kinematic Equations

Intro to Moment of Inertia

Energy of Rolling Motion

Conservation of Energy in Rolling Motion

Moment of Inertia via Integration

Rotational Dynamics with Two Motions

Moment of Inertia & Mass Distribution

Conservation of Energy with Rotation

Parallel Axis Theorem

Moment of Inertia of Systems

General Chemistry

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General Biology

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Financial Accounting

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Building Great Presentations

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Critical Thinking And Problem Solving

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Habits To Win Every Day

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How To Influence & Persuade

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Leadership Skills For Rising Stars

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Mistakes To Avoid When Resolving Conflict

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Winning Collaboration: How To Work More Effectively With Different Personalities

Writing Emails People Want To Read

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Introduction to Python

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Agile Project and Product Management

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Introduction to Microsoft Power BI

Microsoft Power BI

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Data Analysis Fundamentals with Excel

Data Analysis - Excel

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Getting Started with  and Cryptocurrency

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HTML, CSS & Layout

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Learn Enough JavaScript to be Dangerous: A Tutorial Introduction to Programming with JavaScript