Conservation of Angular Momentum

Definition

Conservation of angular momentum is a fundamental principle in physics that states the total angular momentum of a closed system remains constant unless an external torque is applied. This principle governs the rotational motion of objects and is crucial in understanding the dynamics of rotating systems.

5 Must Know Facts For Your Next Test

1. Conservation of angular momentum states that the total angular momentum of a closed system remains constant unless an external torque is applied.
2. In the absence of external torques, the angular momentum of a rotating object is conserved, even if the object's shape or size changes.
3. When an object's moment of inertia decreases, its angular velocity must increase to conserve angular momentum, and vice versa.
4. Conservation of angular momentum explains phenomena such as the increase in an ice skater's rotational speed when they pull their arms in, and the precession of a spinning top.
5. The principle of conservation of angular momentum is a fundamental law of physics and is used in the analysis of a wide range of rotational motion problems.

Review Questions

• Explain how the conservation of angular momentum is related to the rotational motion of an object.
  • The conservation of angular momentum states that the total angular momentum of a closed system remains constant unless an external torque is applied. This means that if an object's moment of inertia changes, its angular velocity must change in the opposite direction to conserve the total angular momentum. For example, as an ice skater pulls their arms in, their moment of inertia decreases, causing their angular velocity to increase in order to conserve the total angular momentum of the system.
• Describe how the principle of conservation of angular momentum can be used to analyze the motion of a spinning top.
  • The precession of a spinning top is an example of the conservation of angular momentum in action. As the top spins, it experiences a gravitational torque that tries to rotate it downward. However, the top's angular momentum causes it to precess, or wobble, around the vertical axis instead of falling over. This precession occurs because the top's angular momentum is conserved, and the gravitational torque causes the axis of rotation to change direction rather than the top to simply fall over.
• Analyze how the conservation of angular momentum can be used to explain the behavior of a figure skater performing a spin.
  • $$\text{When a figure skater performs a spin, they are demonstrating the conservation of angular momentum. As the skater pulls their arms and legs in towards their body, their moment of inertia decreases. According to the principle of conservation of angular momentum, this decrease in moment of inertia must be accompanied by an increase in the skater's angular velocity in order to maintain the same total angular momentum. This is why the skater appears to spin faster as they tuck their limbs in closer to their body. Conversely, when the skater extends their limbs, their moment of inertia increases, causing their angular velocity to decrease in order to conserve the total angular momentum of the system.}$$

Related terms

Angular Momentum: Angular momentum is a measure of the rotational motion of an object, defined as the product of the object's moment of inertia and its angular velocity.

Moment of Inertia: Moment of inertia is a measure of an object's resistance to changes in its rotational motion, and depends on the object's mass distribution.

Torque: Torque is the rotational force that causes an object to rotate about an axis, fulcrum, or pivot, and is the product of the force and the perpendicular distance from the line of action of the force to the axis of rotation.