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P211 Final Sample 1
15) A cylinder of mass M = 1.5 kg can rotate about its central axis through point O. Forces are
applied as in the figure below: F 1 = 12 N, F 2 = 8 N, F 3 = 4 N, and F 4 = 5 N.
Also, R 1 = 5 cm and R 2 = 10 cm. The cylinder is solid, has uniform density and radius 10 cm.
What is the magnitude of the angular acceleration of the cylinder, assuming that the forces
maintain their same angles relative to the cylinder during the rotation? (Hint: what is the total torque
on the cylinder from all forces?)
A) 19.03 rad/s 2 B) 26.67 rad/s 2 C) 81.48 rad/s 2
D) 101.3 rad/s 2 E) 240.7 rad/s 2
16) A hollow cylinder and a solid cylinder have the same diameter and the same mass. Each is
placed at rest at the top of a rough inclined plane (with friction!) and each rolls without slipping to
the bottom. Which object has the lesser center of mass velocity when it reaches the bottom of the
plane? (Hint: the moment of inertia of a solid cylinder is smaller than that of a hollow cylinder of the
same mass and diameter.)
A) The solid cylinder.
B) The hollow cylinder.
C) They have the same speed.
D) Impossible to say, since it depends on the angle of the ramp.
E) Impossible to say, since it depends on the coefficient of static friction between the cylinders and
the ramp.
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