Rotational Kinetic Energy, Torque & Work (6.1, 6.2)
The rotational kinetic energy of a wheel rotating at 20rev/s is 1600π² J. Which of the following is most nearly the rotational inertia of the wheel?
A. 1kg•m²
B. 2kg•m²
C. 4kg•m²
D. 4π²kg•m²
B. 2kg•m²
Identical net torques act for the same duration on two solid disks of different rotational inertia
Which of the following correctly describes the change in angular momentum of the disks?
A. The change in angular momentum will be greater for the disk with the smaller rotational inertia.
B. The change in angular momentum will be greater for the disk with the larger rotational inertia.
C. The change in angular momentum will be equal for both disks.
D. The change in angular momentum will be zero for both disks.
C. The change in angular momentum will be equal for both disks.
C. mvL
A bowling ball of mass 5.0 kg and radius 12.0 cm rolls along a horizontal surface with a velocity of 8 m/s. The ball is a solid sphere with a rotational inertia of I=(2/5)mr².
Which of the following is most nearly the total kinetic energy of the bowling ball?
A. 60 J
B. 120 J
C. 160 J
D. 220 J
D. 220 J
Q: Where did the wheel tell the other wheel where he hit her while they were sitting still?
A: In-her-shin!
(Get it? Inertion? In her shin? Inertia? 🤣 Laugh please)
A solid disc and a solid sphere of mass M and radius R spin about their central axes with the same angular velocity. The rotational inertia of a solid disc is (1/2)MR², and rotational inertia of a solid sphere is (2/5)MR².
Which of the following statements is true about the rotational kinetic energies of the disc and sphere?
A. The disc has a greater rotational kinetic energy than the sphere.
B. The sphere has a greater rotational kinetic energy than the disc.
C. The disc and the sphere have the same rotational kinetic energy.
D. There is not enough information to compare the rotational kinetic energies of the disc and sphere.
A. The disc has a greater rotational kinetic energy than the sphere.
A wheel initially rotates about its center with a constant angular speed in the clockwise direction. A constant force F₀ is exerted on the wheel on its side.
Which of the following correctly describes the angular impulse on the wheel at the moment the force is applied?
A. The angular impulse is zero.
B. The angular impulse is in the clockwise direction.
C. The angular impulse is in the counterclockwise direction.
D. The direction of the angular impulse cannot be determined.
C. The angular impulse is in the counterclockwise direction.
An object moving with linear momentum pᵢ collides with the end of a thin uniform rod of length x, as shown in the figure. After the collision, the object rebounds with linear momentum pᶠ, and the rod rotates about a pivot at its other end.
Which of the following gives the magnitude of the angular momentum of the rod after the collision?
A. pᶠ-pᵢ
B. pᶠ+pᵢ
C. (pᶠ-pᵢ)x
D. (pᶠ+pᵢ)x
C. (pᶠ-pᵢ)x
B. Satellite X has more kinetic energy and less potential energy than satellite Y.
A: Because they all started torque-ing when the ball dropped!
A fairground wheel of radius 15 m and mass 4×10⁵ kg is mounted on the fixed, frictionless axle of a motor. The wheel can be modeled as a hoop of rotational inertia MR². The motor increases the angular speed of the wheel from rest to a maximum value of 0.35rad/s in 25.0 seconds.
Which of the following is most nearly the average power output of the motor?
A. 2.2×10⁵ W
B. 4.4×10⁵ W
C. 6.3×10⁵ W
D. 1.3×10⁵ W
A. 2.2×10⁵ W
A solid disk of rotational inertia 0.5 kg∙m² spins with an angular momentum of 4 kg∙m². The disk experiences an angular impulse for a duration of 8 seconds which reduces its angular speed by half.
Which of the following is most nearly the net torque applied to the disk?
A. 0.25 N∙m
B. 0.5 N∙m
C. 1.0 N∙m
D. 1.25 N∙m
A. 0.25 N·m
A spherical star of mass M and radius R rotates about its axis. It has a rotational inertia of (2/5)MR². The star explodes, ejecting mass in space radially and symmetrically. The remaining star is left with a mass of (1/10)M and a radius of (1/50)R.
What is the ratio of the star's final angular velocity to its initial angular velocity?
A. 1/25000
B. 1/500
C. 500
D. 25000
D. 25000
C. The solid cylinder, because it gains less rotational kinetic energy than the hollow cylinder.
Q: Why did the frog become a rigid system?
A: Because it saw a fly-wheel!
When a force of 60 N is applied normally to the end of the wrench to tighten a bolt, it turns through an angle of 45°.
Which of the following is most nearly the work done on the bolt if the distance from the end of the wrench to the center of the bolt is 22 cm ?
A. 5 J
B. 9 J
C. 10 J
D. 20 J
C. 10 J
A constant force of 250 N is applied tangentially to the outer edge of a playground merry-go-round of radius 2.0 m to rotate it from rest. A frictional force of 50 N is exerted tangentially at a distance of 25 cm from the axis of rotation. The rotational inertia of the merry-go-round is 1500 kg∙m².
Which of the following is most nearly the angular speed of the merry-go-round if the force is applied for 5 seconds?
A. 0.17 rad/s
B. 0.33 rad/s
C. 1.3 rad/s
D. 1.6 rad/s
D. 1.6 rad/s
A ball of mass 50 g is thrown at a door of mass 20 kg . The ball strikes the center of the door perpendicularly with a velocity of 20 m/s and rebounds at 15 m/s. The door has a height of 200 cm and a width of 80 cm .
Taking the rotational inertia of the door about its hinges as (1/3)ML², which of the following is most nearly the angular speed of the door after the collision?
A.0.02 rad/s
B. 0.08 rad/s
C. 0.16 rad/s
D. 0.40 rad/s
D. 0.40 rad/s
A probe is launched vertically upwards from the Earth's surface with a velocity equal to half the required escape velocity from this point.
If the radius of the Earth is R, which of the following expressions correctly describes the maximum height reached by the probe?
A. R/3
B. R/2
C. R
D. 2R
A. R/3
Q: What do you call it when someone does something out of being irresistibly compelled to a high degree?
A: An angular impulse!
A uniform rod of length L and mass M is initially held vertically with one end resting on the horizontal ground. When the rod is released from rest, the upper end falls to the ground, and the lower end does not slip. The rotational inertia of the rod about one of its ends is (1/3)ML².
Which of the following expressions represents the linear velocity of the upper end of the rod immediately before it strikes the floor?
A. √(2g/L)
B. √(3g/L)
C. √(2gL)
D. √(3gL)
D. √(3gL)
A uniform rod of length L = 2.0 m and mass M = 4.0 kg lies motionless on a frictionless horizontal table. A small steel ball of mass m = 1.0 kg travels horizontally at 6.0 m/s and strikes the end of the rod perpendicularly, sticking to it (perfectly inelastic collision). The ball hits the rod at a right angle to its length and sticks to the rod's end.
After the collision, the rod and ball rotate together about the rod’s center of mass (which shifts due to the mass of the ball). Ignore vertical motion.
What is the angular speed ω of the system immediately after the collision?
Hint: Remember center of mass formula, parallel-axis theorem, and point mass moment of inertia.
A. 1.1 rad/s
B. 1.7 rad/s
C. 2.0 rad/s
D: 2.25 rad/s
D: 2.25 rad/s
A pottery wheel with a rotational inertia of 8.2 kg∙m² rotates at a constant rate of 22 rpm. The artist drops a lump of clay of mass 1.8 kg on the wheel, where it sticks at a distance of 46.0 cm from the axis of rotation.
If no net external torque acts on the system, which of the following is most nearly the angular speed of the wheel after the clay is dropped on it?
A. 2.1 rad/s
B. 2.2 rad/s
C. 2.3 rad/s
D. 2.4 rad/s
B. 2.2 rad/s
A solid ball of mass M and radius R has rotational inertia (4/5)MR² about its center. It rolls without slipping along a level surface at speed v just before it begins rolling up an inclined plane.
Which of the following expressions correctly represents the maximum vertical height the solid ball can ascend to when it rolls up the incline without slipping?
A. v²/(5g)
B. (2v²)/(5g)
C. v²/(2g)
D. (7v²)/(10g)
D. (7v²)/(10g)
A: Because then she would have to admit she was rolling without slipping!