PHYS 6A Lecture Notes - Lecture 19: Rotational Energy, Angular Velocity

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14 Mar 2019

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PHYS 6A Lecture Notes - Lecture 17: Angular Acceleration, Bicycle Wheel, Radian

PHYS 6A Lecture Notes - Lecture 19: Rotational Energy, Angular Velocity

PHYS 6A Lecture Notes - Lecture 20: Elastic Modulus

Document Summary

A triangular shape is made from identical balls and identical rigid massless rods. The moment of inertia about the a, b and c axes is i a , i b , i c , respectively. I = md^2 + md^2 + md^2. 3 objects with the same mass and the outer radius. Each object is rotating about its axis of symmetry. All three objects have the same rotational kinetic energy. Two spinning disks have the same mass, but disk 2 has double the radius of disk 1. (they both have the same kinetic energy of rotation) The total kinetic energy of a rolling object is the sum of its linear and rotational kinetic energies. A hoop has a mass of 145 kg. The hoop rolls without slipping along a horizontal plane. If the center of mass of the hoop has a speed of 0. 305 m/s.

Related Questions

The moment of inertia of a uniform-density disk rotating about anaxle through its center can be shown to be (1/2)MR2. This result isobtained by using integral calculus to add up the contributions ofall the atoms in the disk (see Problem 9.3). The factor of 1/2reflects the fact that some of the atoms are near the center andsome are far from the center; the factor of 1/2 is an average ofthe square distances. A uniform-density disk whose mass is 15 kgand radius is 0.15 m makes one complete rotation every 0.3 s.

(a) What is the moment of inertia of this disk?
I = kgÂ·m2
(b) What is its rotational kinetic energy?
Krot = J
(c) What is the magnitude of its rotational angular momentum?
Lrot = kgÂ·m2/s

what is the final angular velocity, ωf, of the two disks? express ωf in terms of it, ir, and ωi.

Consider a turntable to be a circular disk of moment of inertia It rotating at a constant angular velocity ωi(note that angular velocities use the Greek letteromega and not double-u) around an axis through the center and perpendicular to the plane of the disk (the disk's "primary axis of symmetry") as shown in(Figure 1) . The axis of the disk is vertical and the disk is supported by frictionless bearings. The motor of the turntable is off, so there is no external torque being applied to the axis.

Another disk (a record) is dropped onto the first such that it lands coaxially (the axes coincide). The moment of inertia of the record is Ir. The initial angular velocity of the second disk is zero.

There is friction between the two disks.

After this "rotational collision," the disks will eventually rotate with the same angular velocity.

Part A

What is the final angular velocity, ωf, of the two disks?

Express ωf (omega subscript f) in terms of It, Ir, and ωi (omega subscript i).

Part B

Because of friction, rotational kinetic energy is not conserved while the disks' surfaces slip over each other. What is the final rotational kinetic energy, Kf, of the two spinning disks?

Express the final kinetic energy in terms of It, Ir, and the initial kinetic energy Ki of the two-disk system. No angular velocities should appear in your answer.

violetclam954

Consider a turntable to be a circular disk of the moment of inertia I_t rotating at a constant angular velocity ωi(note that angular velocities use the Greek letter omega and not double-u) around an axis through the center and perpendicular to the plane of the disk (the disk's "primary axis of symmetry") as shown in(Figure 1). The axis of the disk is vertical and the disk is supported by frictionless bearings. The motor of the turntable is off, so there is no external torque being applied to the axis.

Another disk (a record) is dropped onto the first such that it lands coaxially (the axes coincide). The moment of inertia of the record is Ir. The initial angular velocity of the second disk is zero.

There is friction between the two disks.

After this "rotational collision," the disks will eventually rotate with the same angular velocity.

Part A

What is the final angular velocity, ωf, of the two disks?

Express ωf (omega subscript f) in terms of It, Ir, and ωi (omega subscript i).

Part B

Because of friction, rotational kinetic energy is not conserved while the disks' surfaces slip over each other. What is the final rotational kinetic energy, Kf, of the two spinning disks?

taupehamster183

PHYS 6A Lecture Notes - Lecture 19: Rotational Energy, Angular Velocity

PHYS 6A Lecture Notes - Lecture 17: Angular Acceleration, Bicycle Wheel, Radian

PHYS 6A Lecture Notes - Lecture 19: Rotational Energy, Angular Velocity

PHYS 6A Lecture Notes - Lecture 20: Elastic Modulus

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