AP Physics 1 angular momentum conservation key terms

What is angular momentum?

Angular momentum ($\displaystyle L$) is the product of an object's moment of inertia ($\displaystyle I$) and its angular velocity ($\displaystyle heta$). Formula: $\displaystyle L = I heta$.

True or False: Angular momentum is conserved in an isolated system.

True. In the absence of external torques, the total angular momentum of a system remains constant.

Define moment of inertia (I).

Moment of inertia ($\displaystyle I$) quantifies an object's resistance to angular acceleration, depending on mass distribution. Formula: $\displaystyle I = \frac{1}{2} m r^2$ for a solid cylinder.

Fill in the blank: Angular momentum is the product of __________ and angular velocity.

moment of inertia

What is the relationship between torque and angular momentum?

Torque ($\displaystyle au$) is the rate of change of angular momentum. Formula: $\displaystyle au = \frac{dL}{dt}$.

Compare linear momentum and angular momentum.

- Linear momentum ($\displaystyle p$): $\displaystyle p = mv$ - Angular momentum ($\displaystyle L$): $\displaystyle L = I heta$ - Both conserved in isolated systems.

What is the significance of a rotating figure skater pulling in their arms?

The skater decreases their moment of inertia ($\displaystyle I$), resulting in an increase in angular velocity ($\displaystyle heta$) to conserve angular momentum.

When is angular momentum conserved?

Angular momentum is conserved when no external torques act on the system.

True or False: Angular momentum depends on the choice of origin.

True. Angular momentum can vary based on the reference point used to calculate it.

Calculate the angular momentum of a disk with radius 0.5 m and mass 2 kg.

First, find $\displaystyle I$: $\displaystyle I = \frac{1}{2} (2)(0.5^2) = 0.25$ kg·m². If $\displaystyle heta = 1$ rad/s, then $\displaystyle L = 0.25 imes 1 = 0.25$ kg·m²/s.

What role does angular velocity play in angular momentum?

Angular velocity ($\displaystyle heta$) is directly proportional to angular momentum. Greater $\displaystyle heta$ leads to greater $\displaystyle L$ if $\displaystyle I$ remains constant.

Describe the conservation of angular momentum in a closed system.

In a closed system, the total angular momentum before an event equals the total angular momentum after, assuming no external torques.

What happens when a rotating object experiences an external torque?

When an external torque acts on a rotating object, its angular momentum changes according to the torque applied.

Identify two factors affecting angular momentum.

- Moment of inertia ($\displaystyle I$) - Angular velocity ($\displaystyle heta$)

Fill in the blank: The unit of angular momentum is __________.

kg·m²/s

True or False: The angular momentum of a point mass can be zero.

True. If the point mass is at the axis of rotation, its angular momentum is zero.

Figure skater pulls arms in, what happens?

The skater spins faster. Conservation of angular momentum: moment of inertia decreases, angular velocity increases.

True or False: Angular momentum is conserved in a closed system.

True. Angular momentum is conserved when no external torque acts on the system.

Example of angular momentum conservation in sports?

A diver tucking in during a somersault rotates faster. Reduces moment of inertia, increases angular velocity.

Fill in the blank: A spinning figure skater's arms out increase moment of _____.

Inertia. Arms out mean larger radius, thus greater moment of inertia.

How does a merry-go-round demonstrate angular momentum?

As children move toward the center, the rotation speed increases. Angular momentum remains constant.

Cause → Effect: Pulling legs in while spinning.

Cause: Decreased moment of inertia. Effect: Increased angular velocity.

Compare: Ice skater vs. gymnast, angular momentum?

Both conserve angular momentum. Ice skater spins faster by pulling in arms; gymnast does flips by tucking.

Example of angular momentum in car driving?

A car making a turn maintains speed. The car’s wheels generate angular momentum, helping it steer.

How does a rotating planet demonstrate angular momentum?

Earth's rotation maintains angular momentum, affecting day length and climate patterns.

What happens when a spinning object loses mass?

Angular velocity increases. Since angular momentum is conserved, a decrease in mass results in a higher spin rate.

True or False: Angular momentum can be created.

False. Angular momentum can only be transferred or conserved, not created in a closed system.

How does a bike rider conserve angular momentum while turning?

They lean into the turn. Shifting mass keeps the center of mass closer to the rotation axis.

Real-world example of angular momentum in amusement parks?

Ferris wheels maintain angular momentum to keep a steady rotation. The design helps balance forces.

What happens during a collision of spinning objects?

Angular momentum is transferred between objects. Total angular momentum before equals total after the collision.

Explain angular momentum in planetary orbits.

Planets maintain angular momentum around stars. As they orbit, gravitational forces keep their paths stable.

How do ice skaters utilize angular momentum?

Ice skaters maintain speed and balance by pulling in their arms, reducing moment of inertia, thereby increasing angular velocity to conserve angular momentum. This allows them to spin faster during performances.