Chapter 20: Problem 23
What happens to the rotation rate of a pulsar as time passes?
Short Answer
Expert verified
A pulsar's rotation rate decreases over time due to energy loss from radiation.
Step by step solution
01
Understand Pulsar Rotation
Pulsars are rapidly rotating neutron stars emitting beams of radiation. As they rotate, these beams sweep across the Earth, seen as pulsating sources of light.
02
Use Conservation of Angular Momentum
The principle of conservation of angular momentum states that if no external torque acts on a system, its angular momentum remains constant. However, pulsars gradually lose energy over time due to radiation.
03
Consider Energy Loss
As a pulsar emits radiation, it loses energy, which translates to a decrease in rotational kinetic energy. This affects its angular velocity and thus its rotation rate.
04
Determine Rotation Rate Change
Since the pulsar loses energy and its angular momentum remains constant, it must reduce its angular velocity (rotation rate) to compensate. Therefore, its rotation rate slows.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Neutron Stars
Neutron stars are the remnants of massive stars that have undergone supernova explosions. Imagine a star that was initially many times larger than our sun collapsing under its own gravity. When this happens, the core compresses to an incredibly dense state, forming a neutron star.
- Neutron stars are only about 20 kilometers in diameter, roughly the size of a city.
- Despite their small size, they can have a mass about 1.4 times that of the Sun!
- Their density is so extreme that a sugar-cube-sized amount of neutron star material weighs as much as Mount Everest.
Conservation of Angular Momentum
The conservation of angular momentum is a fundamental principle in physics that affects rotating bodies, like pulsars. According to this principle, a system's angular momentum will remain constant unless acted upon by an external torque.
- Angular momentum is the rotational equivalent of linear momentum and depends on the object's mass, rotation speed, and radius.
- In the case of a pulsar, as long as there is no significant external force acting on it, its total angular momentum remains the same over time.
- The equation for angular momentum is given by: \[ L = I \cdot \omega \]where \( L \) is the angular momentum, \( I \) is the moment of inertia, and \( \omega \) is the angular velocity.
Angular Velocity
Angular velocity is a measure of how quickly an object rotates or revolves relative to another point. In the context of pulsars, it plays an essential role since it directly affects how often their beams sweep past our observation point on Earth.
- It is expressed in radians per second and influences the pulsar's rotation rate.
- As the rotational kinetic energy of a pulsar decreases due to energy loss, its angular velocity also decreases.
- The decrease in angular velocity leads to a slower rotation rate, causing the pulsar's pulses to appear less frequent over time.
Rotational Kinetic Energy
Rotational kinetic energy is the energy an object possesses due to its rotation. For pulsars, this energy is critical because it powers their emissions.
- The formula for rotational kinetic energy is: \[ KE_{rot} = \frac{1}{2} I \omega^2 \]where \( KE_{rot} \) is the rotational kinetic energy, \( I \) is the moment of inertia, and \( \omega \) is the angular velocity.
- As pulsars emit radiation, they lose rotational kinetic energy, resulting in a decrease in their angular velocity.
- This energy loss is gradual and causes the pulsar's rotation rate to slow down over time.