Question

The dimensional formula of angular velocity \[\left( \omega =\dfrac{v}{r} \right)\] is
A. \[M{{L}^{\circ }}{{T}^{-2}}\]
B. \[ML{{T}^{-1}}\]
C. \[{{M}^{0}}{{L}^{0}}{{T}^{-1}}\]
D. \[M{{L}^{\circ }}{{T}^{1}}\]

Answer 1

Hint: Angular velocity is the pace of velocity at which an item or a molecule is turning around a middle or a particular point in a given timeframe. It is otherwise called rotational velocity.

Complete answer:
The correct answer is C.
Angular Velocity = Angular displacement\[\times \text{ }{{\left[ Time \right]}^{-1}}~~\]----equation (1)
The dimensional formula of Angular displacement = [\[{{M}^{0}}~{{L}^{0~}}{{T}^{0}}]\] ----equation (2)
And, the dimensions of time = \[[{{M}^{0}}~{{L}^{0~}}{{T}^{1}}]~\]----equation (3)
On substituting the equation (3) and (2) in equation (1) we get,
Angular Velocity = Angular displacement \[\times \text{ }{{\left[ Time \right]}^{-1}}~~\]
\[v\text{ }=~{{[{{M}^{0}}~{{L}^{0~}}{{T}^{0}}\left] \text{ }\times \text{ } \right[{{M}^{0}}~{{L}^{0~}}{{T}^{1}}]}^{-1}}~=\text{ }[{{M}^{0}}~{{L}^{0~}}{{T}^{-1}}]\]
Therefore, the angular velocity is dimensionally represented as \[{{M}^{0}}{{L}^{0}}{{T}^{-1}}\]
Angular velocity assumes a vital role in the rotational movement of an object. We definitely realize that in an item indicating rotational movement all the particles move all around. The straight velocity of each partaking molecule is legitimately identified with the angular velocity of the entire object.
Angular velocity is estimated in edge per unit time or radians every second (\[\dfrac{radian}{\sec .}\]). The pace of progress of angular velocity is angular speeding up. Let us learn in more insight concerning the connection between angular velocity and direct velocity, angular dislodging and angular increasing speed.
These two end up as vector items comparative with one another. Fundamentally, the angular velocity is a vector amount and is the rotational speed of an article. The angular removal in a given timeframe gives the angular velocity of that object.
For an article pivoting about a hub, each point on the item has the equivalent angular velocity. The unrelated velocity of any point is corresponding to its good ways from the pivot of turn.

Note: Angular velocity has the units \[\dfrac{radian}{\sec }\]. Essentially the pace of progress of angular uprooting is called angular velocity. Similarly, the pace of progress of direct relocation is called linear velocity.