This is the question: Designate these statements as True or False. Your response

Question

This is the question: Designate these statements as True or False. Your responsemust be thorough and complete with equations and explanations usingunderying basic concepts and principles. (This is what theprofessor is looking for.) (a) Just like mass the moment of inertia of an object remainsa constant. (b) The earth's rotational kinetic energy resulting fromits daily spin on its own axis remains a constant. *I know (a) is false and (b) is true but can you giveme a thorough explanations why please. This is the question: Designate these statements as True or False. Your responsemust be thorough and complete with equations and explanations usingunderying basic concepts and principles. (This is what theprofessor is looking for.) (a) Just like mass the moment of inertia of an object remainsa constant. (b) The earth's rotational kinetic energy resulting fromits daily spin on its own axis remains a constant. *I know (a) is false and (b) is true but can you giveme a thorough explanations why please.

Explanation / Answer

A is true only if the distance from the axis of rotation remainsconstant, therefore it is false. The moment of inertia is givenby I = kmr2 where k is a constant called the inertia constant that varies withthe object. Inertia is the rotational analog of mass. It describes thedifficulty of changing the objects motion about an axis. The momentof inertia can change if the shape of the object changes or if theradius changes. For example, a person spinning in a circle willhave different moments of inertia depending on if their arms areoutstretched or held close to the body. Rotational kinetic energy is the kinetic energy due to the rotationof an object. It is given by the equation K = 1/2 I2 So as long as the angular velocity, , remains constant therotational kinetic energy should also remain constant. The inertiashould be constant since the shape of the earth does not change andits distance from the axis remains the same.

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