31) A solid disk of radius 1.60 m and mass 2.30 kg rolls without slipping to the bottom of an inclined plane. If the angular velocity of the disk is 4.27 rad/s at the bottom, what is the height of the inclined plane?
A) 3.57 m
B) 2.68 m
C) 3.14 m
D) 4.28 m
32) In Figure 9.4 are scale drawings of four objects, each of the same mass and uniform thickness. Which has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing? In each case the axis passes through point P.
E) The moment of inertia is the same for all of these objects.
Short Answer Questions
1) A bicycle wheel has an initial angular velocity of 7.2 rad/s. After turning through one-half of a revolution, the angular velocity is reduced to 2.2 rad/s. If the angular acceleration of the wheel is constant during the motion, how long will it take the wheel to make the one-half revolution?
2) In Figure 9.5, a rope is wrapped around a wheel of radius R = 2.0 meters. The wheel is mounted with frictionless bearings on an axle through its center. A block of mass 14 kg is suspended from the end of the rope. When the system is released from rest it is observed that the block descends 10 meters in 2.0 seconds. What is the moment of inertia of the wheel?
3) A futuristic design for a car is to have a large disk-like flywheel within the car storing kinetic energy. The flywheel has mass 370 kg with a radius of 0.50 m and can rotate up to 200 rev/s. Assuming all of this stored kinetic energy could be transferred to the linear velocity of the 1500-kg car, find the maximum attainable speed of the car.
4) In Figure 9.6, a weightlifter’s barbell consists of two identical small but dense spherical weights each of mass 50 kg. The weights are connected by a 0.96 m steel rod with mass of 24 kg. Find the moment of inertia of the barbell through the axis at the center, assuming the two weights are small enough to be treated as point masses.
5) A marble that is rolling without slipping approaches a hill traveling at 8.50 m/s. How high vertically will the marble go (a) if the hill is rough enough to prevent any slipping, and (b) if the hill is perfectly smooth? (c) Why does the marble rise to different heights when it had the same initial kinetic energy in both cases?
6) A solid uniform 3.33 kg disk has string of negligible mass wrapped around its rim, with one end of the string tied to the ceiling, as shown in Figure 9.7. The disk is released from rest and turns as it falls as the string unwraps. At the instant its center has fallen 2.25 m, (a) how fast is it moving, and (b) how much rotational kinetic energy does it have?
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