Question

The apparatus is initially at rest on a nearly frictionless surface. then you pull the string with a constant force f. at the instant when the center of the disk has moved a distance d, an additional length w of string has unwound off the disk. (use any variable or symbol stated above as necessary.)at this instant, what is the angular speed of the apparatus?

Answer 1

Step-by-step explanation:

Let mass of the apparatus be m .

applying work-energy theorem

work done = kinetic energy

f x d = 1/2 m v² , v is velocity acquired by apparatus

v =
`\sqrt{(2fd)/(m) }`

The apparatus will start moving on a circular path with radius of w ( additional length of string )

radius of circle = w

velocity on the circular path = v

angular velocity = linear velocity / radius

= v / w

=
`(1)/(w) \sqrt{(2fd)/(m) }`