Relationship between moment of inertia and angular velocity?

What is the relationship between moment of inertia and angular velocity? The formula for moment of inertia is I=mxr^2. What is the relationship to angular velocity? During a pirouette, the rotational speed increases with a smaller moment of inertia…

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PMeindl
9 months ago

Angular velocity x moment of inertia around the axis of rotation = angular momentum. This remains constant, excluding friction losses. During a pirouette, the dancer pulls her arms toward her, thus reducing her moment of inertia.

And if this becomes smaller, the angular velocity must increase so that the angular momentum remains constant!

Franz1957
9 months ago
Reply to  JuanliebtMathe

Das Prinzip der Drehimpulserhaltung ist ein Naturgesetz.

PMeindl
9 months ago
Reply to  JuanliebtMathe

Aus demselben Grund, wie ein bewegter Körper seine Geschwindigkeit und Richtung beibehält, solange keine äußeren Kräfte auf ihn wirken.

hologence
9 months ago

es gilt Drehimpulserhaltung.