Learning Goal: To understand how to use conservation of angular momentum to solve problems involving collisions of rotating bodies. Consider a turntable to be a circular disk of moment of inertia It rotating at a constant angular velocity wi (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 Figure < 1 of 1 Part A What is the final angular velocity, wf, of the two disks? Express wf (omega subscript f) in terms of It, Ir, and wi (omega subscript i). View Available Hint(s) ΠΫΠΙ ΑΣΦ Submit Part B Because of friction, rotational kinetic energy is not conserved while the disks' surfaces slip over each other. What i s the final rotational kinetic energy, Kr, of the two spinning disks? Express the final kinetic energy in terms of It, Ir, and the initial kinetic energy K₁ of the two-disk system. No angular velocities should appear in your answer. ▸ View Available Hint(s) K₁ = Submit [ΕΙ ΑΣΦ 3 ?
Learning Goal: To understand how to use conservation of angular momentum to solve problems involving collisions of rotating bodies. Consider a turntable to be a circular disk of moment of inertia It rotating at a constant angular velocity wi (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 Figure < 1 of 1 Part A What is the final angular velocity, wf, of the two disks? Express wf (omega subscript f) in terms of It, Ir, and wi (omega subscript i). View Available Hint(s) ΠΫΠΙ ΑΣΦ Submit Part B Because of friction, rotational kinetic energy is not conserved while the disks' surfaces slip over each other. What i s the final rotational kinetic energy, Kr, of the two spinning disks? Express the final kinetic energy in terms of It, Ir, and the initial kinetic energy K₁ of the two-disk system. No angular velocities should appear in your answer. ▸ View Available Hint(s) K₁ = Submit [ΕΙ ΑΣΦ 3 ?
College Physics
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
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Transcribed Image Text:## Learning Goal:
To understand how to use conservation of angular momentum to solve problems involving collisions of rotating bodies.
Consider a turntable to be a circular disk of moment of inertia \( I_t \), rotating at a constant angular velocity \( \omega_i \) (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 \( I_r \). 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 together.
### Figure:
The figure shows a side view of a turntable and a disk. The turntable has a moment of inertia \( I_t \) and rotates with an angular velocity \( \omega_i \), and the disk has a moment of inertia \( I_r \).
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### Part A
What is the final angular velocity, \( \omega_f \), of the two disks?
**Express \( \omega_f \) in terms of \( I_t \), \( I_r \), and \( \omega_i \).**
(The input box for the answer is shown here with a submit button.)
---
### 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, \( K_f \), of the two spinning disks?
**Express the final kinetic energy in terms of \( I_t \), \( I_r \), and the initial kinetic energy \( K_i \) of the two-disk system. No angular velocities should appear in your answer.**
(The input box for the answer is shown here with a submit button.)
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