Imagine that a yo-yo is diagramed as a falling object that rotates with a string
ID: 1775492 • Letter: I
Question
Imagine that a yo-yo is diagramed as a falling object that rotates with a string attached on one end. Assuming that the string provides a constant upwards tension force on the yo-yo:
1) Utilizing the principles you know from Newton's second law, set up an equation for the acceleration of the yo-yo. Your answer should involve the variables for the unknown tension (t) and the given mass (c) of the yo-yo.
2) Use the rotational (angular) counterpart of Newton's second law to set up an equation for the rotational acceleration of the yo-yo. Your answer should involve (t) from the above question, the radius (r) of the yo-yo, and its moment of inertia (m).
3) Since the yo-yo is not slipping as it rolls, use the relationship the book provided to relate rotational and linear acceleration (a = R) to relate the equations you found above to solve for the acceleration of the center of the yo-yo.
4) Solve for the acceleration of the yo-yo if it is in the shape of both a solid disk and a hoop.
Explanation / Answer
a) Let the tension in rope = T, m= mass of yo-yp, a= acceleration with which the yo-yo is falling
ma= mg - T
a= ( mg-T)/m
T = m (g-a)
b) Tr = I ( I am using I for moment of inertia to avoid confusion)
= Tr / I
c) a = R
a= R ( Tr/I)
a= TR^2/ I
cd) I for solid disk = 1/2 MR^2
a= 2T/m
I for hoop= mr^2
a= T/m