| 8 | | A bucket filled with water has a mass of 23 kg and is attached to a rope, which in turn, is wound around a 0.050-m radius cylinder at the top of a well. What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate? (g = 9.8 m/s2) | 11 Nm |
| 8 | | A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder at the top of a well. A crank with a turning radius of 0.25 m is attached to the end of the cylinder and the moment of inertia of cylinder and crank is 0.12 kg×m2. If the bucket is raised to the top of the well and released, what is the acceleration of the bucket as it falls toward the bottom of the well? (Assume rope's mass is negligible, that cylinder turns on frictionless bearings and that g = 9.8 m/s2.) | 3.2 m/s^2 |
| 8 | | A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder at the top of a well. The bucket is raised to the top of the well and released. The bucket is moving with a speed of 8.0 m/s upon hitting the water surface in the well. What is the angular speed of the cylinder at this instant? | 160 rad/s |
| 8 | | A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder, with crank, at the top of a well. The moment of inertia of the cylinder and crank is 0.12 kg*m^2. The bucket is raised to the top of the well and released to fall back into the well. What is the kinetic energy of the cylinder and crank at the instant the bucket is moving with a speed of 8.0 m/s? | 1.5*10^3 J |
| 8 | | A bucket of water with total mass 23 kg is attached to a rope, which in turn, is wound around a 0.050-m radius cylinder at the top of a well. A crank with a turning radius of 0.25 m is attached to the end of the cylinder. What minimum force directed perpendicular to the crank handle is required to just raise the bucket? (Assume the rope's mass is negligible, that cylinder turns on frictionless bearings, and that g = 9.8 m/s2.) | 45 N |
| 8 | | A bus is designed to draw its power from a rotating flywheel that is brought up to its maximum speed (3 000 rpm) by an electric motor. The flywheel is a solid cylinder of mass 500 kg and radius 0.500 m (Icylinder = MR^2/2). If the bus requires an average power of 10.0 kW, how long will the flywheel rotate? | 308 s |
| 8 | | A cylinder (I = MR^2/2) is rolling along the ground at 7.0 m/s. It comes to a hill and starts going up. Assuming no losses to friction, how high does it get before it stops? | 3.7 m |
| 8 | | A cylinder with its mass concentrated toward the center has a moment of inertia of 0.1 MR2. If this cylinder is rolling without slipping along a level surface with a linear speed v, what is the ratio of its rotational kinetic energy to its linear kinetic energy? | 1/l0 |
| 8 | | A disk has a moment of inertia of 3.0*10^-4 kg×m2 and rotates with an angular speed of 3.5 rad/sec. What net torque must be applied to bring it to rest within 3 s? | 3.5*10^-4 Nm |
| 8 | | A figure skater on ice with arms extended, spins at a rate of 2.5 rev/s. After he draws his arms in, he spins at 6.0 rev/s. By what factor does the skater's kinetic energy change when he draws his arms in? | 2.4 |
| 8 | | A figure skater with arms initially extended starts spinning on the ice at 3 rad/s. She then pulls her arms in close to her body. Which of the following results? | a greater rotational rate |
| 8 | | A gyroscope has a moment of inertia of 0.14 kg×m2 and an initial angular speed of 15 rad/s. Friction in the bearings causes its speed to reduce to zero in 30 s. What is the value of the average frictional torque? | 7.0*10^-2 Nm |
| 8 | | A gyroscope has a moment of inertia of 0.140 kg*m^2 and has an initial angular speed of 15.0 rad/s. If a lubricant is applied to the bearings of the gyroscope so that frictional torque is reduced to 2.00*10-2 N*m, then in what time interval will the gyroscope coast from 15.0 rad/s to zero? | 105s |
| 8 | | A hoop of radius 1.0 m is placed in the first quadrant of an xy-coordinate system with its rim touching both the x-axis and the y-axis. What are the coordinates of its center of gravity? | (1.0, 1.0) m |
| 8 | | A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape. Each baton was 0.80 m long and each ball on the end is 0.20 kg. (Ignore the mass of the rods.) What is the moment of inertia if the arrangement is spun around an axis formed by one of the batons? | 0.064 kg*m^2 |