11. A cylinder of mass M and radius R rolls without slipping on a horizontal sur

Question

11. A cylinder of mass M and radius R rolls without slipping on a horizontal surface with angular speed o. Express the total kinetic energy of the cylinder with respect to its center of mass in terms of M R and o. Iem 0.5 MR 12. (True/ False: The potential energy of a stretched spring is given by 0.5 kx The International Space Station is in a circular orbit about the Earth at an altitude of 380 km. What is its orbital period? 13. 14. True /False The outward force necessary to maintain uniform circular motion is defined as

Explanation / Answer

11) Icm = 0.5MR^2
Moment of inertia about end I = Icm +MR^2 = (3/2)MR^2
Total KE = translation KE +rotational KE
= 0.5Mv^2 +0.5Iw^2
v = RW
KE = 0.5MR^2w^2 +0.5*(3/2)MR^2w^2
KE = (5/4)MR^2w^2
12) h = 380 km
mass of earth m = 5.98*10^24 kg
radius of earth r= 6.38*10^6 m
v = (GM/r)^0.5
v =(6.67*10^-11*5.98*10^24/(6.38*10^6+380000))^0.5
v = 7681 m/s

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