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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define angular velocity in 3D.
π‘ Hint: Think about the difference from 2D.
Question 2
Easy
Explain the relationship between angular momentum and moment of inertia in 3D.
π‘ Hint: Consider the matrix form of inertia.
Practice 1 more question and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does the angular velocity vector represent in 3D?
- It represents a scalar.
- It represents the rate of change of position.
- It describes the rotation direction and speed.
π‘ Hint: Recall how we represent vectors in physics.
Question 2
True or False: In 3D, angular momentum is always parallel to angular velocity.
- True
- False
π‘ Hint: Think based on the previous discussions regarding motion in 3D.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
π‘ Hint: Remember to apply matrix multiplication.
Question 2
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?
π‘ Hint: Think of how it changes in balance and direction once external forces act.
Challenge and get performance evaluation