Practice - Tensor Form
Practice Questions
Test your understanding with targeted questions
Define angular velocity in 3D.
💡 Hint: Think about the difference from 2D.
Explain the relationship between angular momentum and moment of inertia in 3D.
💡 Hint: Consider the matrix form of inertia.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the angular velocity vector represent in 3D?
💡 Hint: Recall how we represent vectors in physics.
True or False: In 3D, angular momentum is always parallel to angular velocity.
💡 Hint: Think based on the previous discussions regarding motion in 3D.
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Challenge Problems
Push your limits with advanced challenges
A rigid body has an angular velocity of \(5 \hat{i} + 2 \hat{j} + 3 \hat{k}\) rad/s. If the moment of inertia tensor is given by \(\mathbf{I} = \begin{pmatrix} 1 & 0 & 0 \ 0 & 2 & 0 \ 0 & 0 & 3 \end{pmatrix}\), calculate the angular momentum vector.
💡 Hint: Remember to apply matrix multiplication.
Describe what happens to a spinning gyroscope's angular momentum as it experiences a change in angular velocity due to external torques. How does its axis of rotation behave?
💡 Hint: Think of how it changes in balance and direction once external forces act.
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Reference links
Supplementary resources to enhance your learning experience.