Suppose you are standing on the center of a merry-go-round that is at rest. you are holding a spinning bicycle wheel over your head so that its rotation axis is pointing upward. the wheel is rotating counterclockwise when observed from above.

for this problem, neglect any air resistance or friction between the merry-go-round and its foundation.

suppose you now grab the edge of the wheel with your hand, stopping it from spinning. what happens to the merry-go- round?

a) it remains at rest.
b) it begins to rotate counterclockwise (as observed from above).
c) it begins to rotate clockwise (as observed from above).
d) cannot be determined from the information given.

B) it begins to rotate counterclockwise (as observed from above).

Explanation:

As we know that there is no external torque on the system of wheel + merry go round

so here angular momentum of the system must be conserved

so initially we know that wheel is rotating and merry go round is stationary in counter clockwise direction

Now when we stop the wheel its net angular momentum will be conserved and the system will still continue to move with some angular speed in the same direction

so finally the merry go round must have to rotate in the counter clockwise direction with some angular speed

so correct answer will be

B) it begins to rotate counterclockwise (as observed from above).

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 .