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$\bullet$ A size-5 soccer ball of diameter 22.6 $\mathrm{cm}$ and mass 426 $\mathrm{g}$rolls up a hill without slipping, reaching a maximum height of5.00 $\mathrm{m}$ above the base of the hill. We can model this ball as athin-walled hollow sphere. (a) At what rate was it rotating atthe base of the hill? (b) How much rotational kinetic energydid it then have?

a) 67.9 $\mathrm{rad} / \mathrm{s}$b) 8.35 $\mathrm{J}$

Physics 101 Mechanics

Chapter 9

Rotational Motion

Physics Basics

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Cornell University

University of Michigan - Ann Arbor

Hope College

University of Winnipeg

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the first part of this question, we are going to kill Colette language mostly of the ball when it reaches at the bottom in order to kill clear the singular of lost E. Let me write few questions. Considering the ball as a whole is fair, we can. I do woman no Phoenicia, as I call to two by three Amar Square so called equation one. We have another equation, which is we call to our omega. So quality quitting, too? No. Using are defined coordinates. We can you find the position off bald. Different points is why close to zero at the bottom off the kill and why I equals tau zero, which is the location off the ball. Time equals to zero and the Y difficult wedge because to 5.0 meter now, using the more conservation off energy we can right care translation initial plus your vision initial plus potential in that initial because too tricycle final plus corroboration final plus potential energy at final position. Now it looks defined. These energies. You are a postal Tzeitel and the transition finally calls to zero equals two generations violent, and you finally calls to MGH. No this question can be routinized transitional initial plus care additional initially goes to you f So call it equating three Quentin three can be returners whenever too. And we squared plus one by two Iomega Square equals to MGH No setting the values off I Andromeda from equation one and two into this equation we even get one by two em we square plus one by two door to buy three m r square in tow We buy our whole square equals to em Judge. Now this question can be simply fight is we People's toe squared off six by five Judge So Kordic waiting for now setting the world goes into this equation four We can night we poles to square it off six by five in tow. My point it we depart skin square in tow 5.0 meter So this is it went to week was to 7.67 meter per second. Now let's kill cleared the Omega Using equation too Maybe equals 27.67 meter per second The wanted by zero point 113 meter. So this will view us my vehicles too 6 to 7 point mine Radian per second. The second part of this question, we are going to kill plate the basement kinetic energy. Let's define the rotation. Kinetic energy care rotational equals to one by two. Iomega Square Now sitting well, you off I into this question. Correctional equals to one by two door to buy three M R Square. Omega Square, which can be read a ledge, cables to one by theme with Square called Equation. Five. While sitting the values into this equation life, we will get current national equals to one by three into 0.4 to 6 kg in tow. Selling 0.67 meter bar sicken holds quit. So this with US care additional equals two 8.35 joke. So this is the answer off second part of this question.

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