Question

1. A yo-yo consists of two solid disks, each of mass M and radius 3R. The two disks are connected by a rod of radius R and negligible mass.

a.) The moment of inertia of the yo-yo about its axis of symmetry is of the form ???^2 where ? is a number. What is ??

b.) Draw the extended free body diagram for the yo-yo and use it to write Newton's 2nd law in terms of the magnitude of the acceleration of the center of mass of the yoyo. Be careful with the mass and pay attention to the direction of the acceleration,

c.) Take the axis of rotation to be the center of mass of the yo-yo. Use your extended free body diagram to write the rotational second law in terms of the magnitude of the angular acceleration ? and the moment of inertia I of the yo-yo. Pay attention to the direction of the acceleration.

d.) Use the relation between the acceleration acm and angular acceleration ? and the relations above to determine the acceleration of the yo-yo.

e.) What is the tension in the string as the yo-yo falls?

f.) Starting from rest, how long does it take for the yo-yo to fall a distance of 0.8 meters?

Comment: the point where the string contacts the yo-yo is momentarily at rest as the string unwinds. Since power P = ?⃗ ⋅ ?⃗ , the fact that ? = 0 at this point, implies that the tension generates zero power and therefore does no work.

Answer 1