There is an analogy between rotational and linear physical quantities. what rotational quantities are analogous to distance and velocity?

ANSWER:

Angular displacement is analogous to distance.

Angular velocity is analogous to velocity.

EXPLANATION:

FOR  ANGULAR DISPLACEMENT AND DISTANCE

Angular displacement = theta

theta = s/r

s = linear dispalcement/distance

r= radius.

so ,

linear displacement/distance  s = theta * r.

FOR  ANGULAR VELOCITY AND VELOCITY

Angular velocity = w

w = v/r

v = velocity

r = radius

so,

velocity v = w * r.

Rotational units can be said to be analogous to linear physical units, for example, linear distance is analogous to angular displacement, since angular displacement is defined as the distance a body travels in a rotary motion.

On the other hand, linear velocity is analogous to angular velocity, since said angular velocity is the angular distance that a body covers per unit of time.

Explanation:

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .