Required information In a Beams ultracentrifuge, the rotor is suspended magnetically in a vacuum. Since there is no mechanical connection to the rotor, the only friction is the air resistance due to the few air molecules in the vacuum. If the rotor is spinning with an angular speed of 3.10 x 10 rad/s and the driving force is turned off, its spinning slows down at an angular rate of magnitude 0.270 rad/s2. During this time, through what angular displacement does the rotor turn? billion revolutions
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.
![**Ultracentrifuge Rotor Dynamics**
In a Beams ultracentrifuge, the rotor is suspended magnetically in a vacuum. Since there is no mechanical connection to the rotor, the only friction is the air resistance due to the few air molecules in the vacuum. If the rotor is spinning with an angular speed of \(3.10 \times 10^5 \, \text{rad/s}\) and the driving force is turned off, its spinning slows down at an angular rate of magnitude \(0.270 \, \text{rad/s}^2\).
**Problem:**
During this time, through what angular displacement does the rotor turn?
- [ ] ____ billion revolutions
This problem encourages exploration of rotational motion and dynamics, considering aspects such as angular speed, angular acceleration, and displacement. Students are prompted to calculate the angular displacement under given conditions, translating the physics into understandable concepts regarding motion in a vacuum with minimal friction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86d5b315-251b-4afc-ade8-02046d912aca%2F0473ba49-0203-4215-bfba-645d373c3e41%2Ftj2uh0e_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
