AP Physics 1 Flashcards: Rotational Inertia

What this deck covers

This deck focuses on Rotational Inertia, giving you a quick way to review the definitions, rules, and examples that matter most for AP Physics 1.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the symbol for rotational inertia?

Answer: Symbol: $I$. Standard physics notation for moment of inertia.

Flashcard 2: State the parallel axis theorem formula.

Answer: $I = I_{\text{cm}} + m d^2$. Relates inertia about any axis to center of mass axis.

Flashcard 3: What is the relationship between torque and rotational inertia?

Answer: $\tau = I \times \beta$. Rotational analog of Newton's second law ($F = ma$).

Flashcard 4: Find the rotational inertia of a point mass at a distance $r$.

Answer: $I = m r^2$. All mass concentrated at distance $r$ from axis.

Flashcard 5: State the formula for rotational inertia of a sphere about its diameter.

Answer: $I = \frac{2}{5} m r^2$. Same as solid sphere about any diameter through center.

Flashcard 6: Identify the formula for rotational inertia of a disk about a tangent axis.

Answer: $I = \frac{3}{2} m r^2$. Uses parallel axis theorem: $\frac{1}{2}mr^2 + mr^2$.

Flashcard 7: Which factor does rotational inertia depend on besides mass?

Answer: Distribution of mass relative to axis. Mass farther from axis increases rotational inertia.

Flashcard 8: How does increasing mass affect rotational inertia?

Answer: Increases rotational inertia. Rotational inertia is directly proportional to mass.

Flashcard 9: What is the rotational inertia of a ring about its diameter?

Answer: $I = \frac{1}{2} m r^2$. Ring rotating about axis through its diameter.

Flashcard 10: Calculate the rotational inertia of a composite object.

Answer: Sum of individual inertias. Add rotational inertias of each component part.

Flashcard 11: What is the formula for rotational inertia of a hollow cylinder?

Answer: $I = m r^2$. Cylindrical shell with all mass at outer radius.

Flashcard 12: What is the formula for rotational inertia of a solid sphere?

Answer: $I = \frac{2}{5} m r^2$. Standard formula for uniform solid sphere rotating about center.

Flashcard 13: What is the rotational inertia of a thin spherical shell?

Answer: $I = \frac{2}{3} m r^2$. Hollow spherical shell about any diameter through center.

Flashcard 14: What is the rotational inertia of a disc about its diameter?

Answer: $I = \frac{1}{4} m r^2$. Disc rotating about axis through its diameter.

Flashcard 15: Calculate the rotational inertia of two masses connected by a rod.

Answer: Use $I = m_1 r_1^2 + m_2 r_2^2$. Treat each mass as point mass at its distance.

Flashcard 16: Calculate the rotational inertia of two point masses at opposite ends of a rod.

Answer: Use $I = m_1 r_1^2 + m_2 r_2^2$. Apply point mass formula to each mass separately.

Flashcard 17: What is the effect of rotational inertia on angular velocity?

Answer: Higher inertia, lower angular velocity. Conservation of angular momentum: $L = I\omega = constant$.

Flashcard 18: What is the relationship between torque and rotational inertia?

Answer: $\tau = I \times \beta$. Rotational analog of Newton's second law ($F = ma$).

Flashcard 19: Identify the formula for rotational inertia of a thin rod about its center.

Answer: $I = \frac{1}{12} m L^2$. For uniform rod rotating perpendicular to length at center.

Flashcard 20: What is the formula for rotational inertia of a thin rod about its end?

Answer: $I = \frac{1}{3} m L^2$. Rod rotating about perpendicular axis at one end.

Flashcard 21: How does increasing the radius affect rotational inertia?

Answer: Increases rotational inertia. Inertia depends on $r^2$, so larger radius increases it.

Flashcard 22: What is the rotational inertia of a solid sphere about a tangent axis?

Answer: $I = \frac{7}{5} m r^2$. Uses parallel axis theorem with $d = r$.

Flashcard 23: Identify the formula for rotational inertia of a solid disc.

Answer: $I = \frac{1}{2} m r^2$. Flat circular disc rotating about its center axis.

Flashcard 24: What is the formula for rotational inertia of a hollow sphere?

Answer: $I = \frac{2}{3} m r^2$. Thin shell with all mass at surface radius.

Flashcard 25: State the effect of rotational inertia on torque requirement.

Answer: Higher inertia, more torque needed. From $\tau = I\alpha$: larger $I$ needs larger $\tau$.

Flashcard 26: What is the effect of doubling radius on rotational inertia?

Answer: Quadruples rotational inertia. Radius appears squared in inertia formulas.

Flashcard 27: What is the effect of mass distribution on rotational inertia?

Answer: Further mass increases inertia. Mass farther from rotation axis contributes more.

Flashcard 28: What is the rotational inertia of a hoop about a tangent axis?

Answer: $I = 2 m r^2$. Uses parallel axis theorem: $I = I_{center} + md^2$.

Flashcard 29: What is the rotational inertia of a thin hoop about its diameter?

Answer: $I = \frac{1}{2} m r^2$. Hoop rotating about perpendicular axis through diameter.

Flashcard 30: State the formula for rotational inertia of a thin hoop about its center.

Answer: $I = m r^2$. All mass concentrated at radius $r$ from center.