Cross Product Torque (with a Cross Product Review)

The video tutorial covers the concept of torque and its calculation using the cross product. It explains the non-commutative nature of the cross product and demonstrates how to solve torque problems using matrices. The tutorial includes examples to illustrate the application of the cross product in determining torque direction and magnitude, emphasizing the use of the right-hand rule. The session concludes with a summary of key points and encourages the use of the cross product for torque calculations.

What is the formula for the magnitude of torque?

• F/r sin theta

• r/F cos theta

• rF sin theta

• rF cos theta

Which rule helps determine the direction of torque?

• Thumb rule

• Right-hand rule

• Left-hand rule

• Index rule

What mathematical operation is used to calculate torque as a vector?

• Dot product

• Subtraction

• Addition

• Cross product

Is the cross product commutative?

• No, never

• No, except in special cases

• Yes, always

• Yes, sometimes

What is the result of A cross B if A = -i + j - 2k and B = 2i - 3j + 4k?

• 0i + 0j + 0k

• 2i - 3j - 4k

• -2i + 0j + k

• -2i + 3j + 4k

In a simple torque example, if the position vector is 1 meter in the x direction and the force is 1 Newton in the y direction, what is the torque direction?

• Positive i direction

• Negative j direction

• Negative k direction

• Positive k direction

What happens to the torque if the force is directed towards the axis of rotation?

• Torque is minimized

• Torque is maximized

• Torque is doubled

• Torque is zero

How does the angle between the position and force vectors affect the torque?

• Torque is independent of the angle

• Torque is maximized at 90 degrees

• Torque is zero at 90 degrees

• Torque is minimized at 180 degrees

Why is the cross product preferred for torque calculation in three dimensions?

• It is more accurate

• It is faster

• It simplifies the calculation

• It avoids the need for angles

What additional step is needed when using the magnitude torque equation in three dimensions?

• Using the cosine rule

• Using the sine rule

• Using the quadratic formula

• Using the Pythagorean theorem