Undergrad Is angle a vector or a scalar quantity?

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SUMMARY

An angle is definitively classified as a scalar quantity, while rotation is categorized as a vector. The angle, such as ##\pi/4##, lacks an inherent direction, distinguishing it from rotation, which possesses both magnitude and direction. However, rotation does not conform to the commutative law of vector addition, as the outcome of two rotations in three dimensions is dependent on the sequence of operations performed.

PREREQUISITES
  • Understanding of scalar and vector quantities
  • Familiarity with angular displacement concepts
  • Basic knowledge of rotational dynamics
  • Comprehension of the commutative law in vector mathematics
NEXT STEPS
  • Research the properties of scalar and vector quantities in physics
  • Explore angular displacement and its applications in mechanics
  • Study the implications of non-commutative operations in rotation
  • Learn about the mathematical representation of rotations in three dimensions
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Students of physics, educators teaching mechanics, and professionals in fields involving rotational dynamics will benefit from this discussion.

Yatin
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Is angle a vector or a scalar quantity?
(eg- θ in l=rθ)
 
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Yatin said:
Is angle a vector or a scalar quantity?
(eg- θ in l=rθ)

An angle itself is a scalar, but a rotation is a vector.

The angle ##\pi/4## has no implied direction as an angle. But, you can have a rotation of ##\pi/4## in any direction.
 
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Likes Dale
Rotation (angular displacement) has a uniquely-defined magnitude and direction, but is not a vector quantity because it doesn't obey the commutative law of vector addition (the result of two rotations in 3 dimensions depends on the order in which you perform them).
 
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Likes Likith D and mfb

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