a) what is the formula for the moment of inertia I of the ring? b)if the ring ro
ID: 1753223 • Letter: A
Question
a) what is the formula for the moment of inertia I of the ring?b)if the ring rolls without slipping on the ramp, what is thequestion for the angular velocity (omega) of the ring in terms of rand v?
c)If the object rolls down 2m of the ramp, what is the change inpotential energy? Leave your answer in therms of theta, m andg.
d)What is the expression for the kinetic energy of the ring?Remember the ring has both rotational and translational kineticenergy forms.
e)Using your expressions from parts b and d, write the kineticenergy as a single term involving just m and v.
f) Using your answers to parts c and e, calculate the finalvelocity of the ring, after it rolls 2 meters down the ramp. Assumethe initial velocity is zero. Reduce your answer so that it is interms of g and theta.
g) Using theta=30 degrees and 9.8m/s2, calculate the final velocityof the ball.
Explanation / Answer
a) what is the formula for the moment of inertia I of the ring? Moment of inertia about an axis passing through the center andperpendicular to its plane M(R2+r2)/2 b)if the ring rolls without slipping on the ramp, what is thequestion for the angular velocity (omega) of the ring in terms of rand v? =v/r c)If the object rolls down 2m of the ramp, what is the change inpotential energy? Leave your answer in therms of theta, m andg. if h is the height of the ramp change in potential energy= mgh-2mgsin d)What is the expression for the kinetic energy of the ring?Remember the ring has both rotational and translational kineticenergy forms. [1/2]*I*2 e)Using your expressions from parts b and d, write the kineticenergy as a single term involving just m and v. 1/2[MV2]{K2/R2} f) Using your answers to parts c and e, calculate the finalvelocity of the ring, after it rolls 2 meters down the ramp. Assumethe initial velocity is zero. Reduce your answer so that it is interms of g and theta. 2gsin g) Using theta=30 degrees and 9.8m/s2, calculate the final velocityof the ball. 2*9.8*0.5=3.130m/sec
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