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Finite rotation can be represented as a vector in three-dimensional space, but it is more accurately described using a rotation matrix or a quaternion. In physics and mathematics, rotations are often treated as transformations rather than simple vectors, as they involve orientation changes rather than just magnitude and direction. While one can use angular displacement vectors, these do not fully capture the properties of rotation, such as the non-commutative nature of rotational operations. Thus, while finite rotation can be associated with a vector-like representation, it is best understood through more complex mathematical structures.
What else can I help you with?
Is rotation scalar or vector?
Rotation is a vector having a direction and magnitude.
Positive rotation of a vector is?
counterclockwise
Is tan x has fourier expansion?
y=tanx cannot be expressed as a Fourier series, since it has infinite number of infinite discontinuity. Dirichlet’s condition or the sufficient condition for a function f(x) to be expressed as a Fourier series. - f(x) is single valued, finite and periodic. - f(x) has a finite number of finite discontinuities. f(x) has a finite number of maxima and minima. - f(x) has no infinite discontinuity.
What is vector in math?
Simply put, a vector is 2 dimensional. Think of speed - it is only one dimensional. It is not a vector, it is a scalar. It is measured in a scale, most commonly noticed when inside a vehicle. You are travelling at 100km/h (60mph) Vectors are 2 dimensional, they have a magnitude and a direction. Think of velocity, as an arrow - imagine you are travelling at 60 mph in a northerly direction, your arrow would be pointing to the notth, with a magnitude of 60mph, If you were travelling at 60mph in a southerly direction, your velocity vector would be pointing towards the south, the exact opposite of your vector if you were travelling in a northerly direction. However the speed in these two scenario's, speed not being a vector, remains exactly the same, 60mph.
How long does it take for complete rotation?
The time it takes for a complete rotation depends on the object in question. For example, Earth takes about 24 hours to complete one rotation on its axis, which defines a day. In contrast, a spinning top may complete a rotation in just a few seconds, depending on its speed and stability. Thus, the duration of a complete rotation varies widely based on the specific context.
Is rotation scalar or vector?
Rotation is a vector having a direction and magnitude.
Why finite angular displacement is not a vector?
No no its a true vector for infinite angular displacement
Why finite angular displacement is not a true vector?
No no its a true vector for infinite angular displacement
Positive rotation of a vector is?
counterclockwise
What is pseudo vector?
A psuedovector is a vector that transform in a proper rotation, but in three dimensions it gains an additional sign flip because of an improper rotation.
Is a torque vector quantity?
Yes. The "direction" of the vector is along the axis of rotation.Yes. The "direction" of the vector is along the axis of rotation.Yes. The "direction" of the vector is along the axis of rotation.Yes. The "direction" of the vector is along the axis of rotation.
What direction does the angular velocity vector of the Earth's rotation point toward?
The Earth's angular velocity vector due to its axial rotation points towards the north pole.
What is an angular velocity scalar or vector?
Angular velocity is a vector quantity that describes the rate of rotation of an object about an axis. It has both magnitude (how fast the object is rotating) and direction (the axis of rotation). Scalar angular velocity only considers the magnitude of the rotation rate without specifying the direction.
What is an affine group?
An affine group is the group of all affine transformations of a finite-dimensional vector space.
Is curl of vector function F must perpendicular to every vector function f?
No, the curl of a vector field is a vector field itself and is not required to be perpendicular to every vector field f. The curl is related to the local rotation of the vector field, not its orthogonality to other vector fields.
Why finite angular displacement are not vectors?
Finite angular displacements are not vectors because they do not adhere to the principles of vector addition and subtraction. While they can be represented as a rotation about a specific axis, they do not possess a unique direction in the same way that linear vectors do. Additionally, angular displacements can lead to ambiguities, such as rotating in opposite directions yielding the same endpoint but different angular values. Therefore, they are better described using concepts like angular momentum or rotation matrices rather than as simple vectors.
Is vector necessarily changed if it is rotated through an angle?
No, a vector is not necessarily changed just by being rotated through an angle. The magnitude and direction of the vector may remain the same even after rotation.
