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## Homework Statement

a) A disk with radius R and mass M is rolling without slipping on a level surface, as shown. The moment of inertia about an axis perpendicular to the page and through the center of the disk is I. If the center of

the disk is moving at speed v, what is the kinetic energy of the disk?

b) For the disk described in part (a), what is the instantaneous speed vL, relative to the ground, of the lowest point on the disk? What is the instantaneous speed vH, relative to the ground, of the highest point on

the disk?

c) Suppose the disk described in part (b) is allowed to roll down an inclined plane, oriented at an angle θ relative to the horizontal, as shown.

Assume that it rolls without slipping, but ignore all frictional effects other than the friction that is necessary to prevent it from slipping. Let g

denote the acceleration of gravity. Calculate the magnitude aCM of the acceleration of the center of mass.

## Homework Equations

## The Attempt at a Solution

part a)

T = .5mv

^{2}+ .5Iw

^{2}

is this right, its barley even a question

part b)

W

_{height}= v/R

W

_{bottom}= -v/R

part c)

mgsinQ - f = ma

fr = .5mr

^{2}[tex]\alpha[/tex]

mgsinQ - .5ma = ma

gsinQ = 3/2 a

a = 2/3 gsinQ