A star rotates in a circular orbit about the center of its galaxy. The radius of the orbit is 4.8 x 1020 m, and the angular speed of the star is 8.1 x 10-15 rad/s. How long (in years) does it take for the star to make one revolution around the center? (b) Number i Units
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.
![**Question:**
A star rotates in a circular orbit about the center of its galaxy. The radius of the orbit is \(4.8 \times 10^{20}\) m, and the angular speed of the star is \(8.1 \times 10^{-15}\) rad/s. How long (in years) does it take for the star to make one revolution around the center?
**Diagram Explanation:**
The diagram shows a spiral pattern representing a galaxy with a circular orbit traced by a star. There are directional arrows indicating the rotation. The radius (\(r\)) of the orbit is marked, emphasizing the circular path around the center of the galaxy.
**Calculation Section:**
(b) The formula to calculate the time for one revolution is \( T = \frac{2\pi}{\omega} \), where \(\omega\) is the angular speed. Convert this time from seconds to years for the final answer.
**Inputs:**
- Number: [Input box]
- Units: [Dropdown selector for units, e.g., years]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9819384-7ac8-4a35-b95a-106c2e89eec6%2F43fbe9d9-564e-42d9-94f5-4709c9ef7f72%2Fhbd09j4_processed.jpeg&w=3840&q=75)
Step by step
Solved in 2 steps
