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 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 2: 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 3: 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 4: What is the relationship between torque and rotational inertia?

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

Flashcard 5: How does increasing mass affect rotational inertia?

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

Flashcard 6: How does increasing mass affect rotational inertia?

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

Flashcard 7: 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 8: 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 9: 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 10: 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 11: What is the unit of rotational inertia in the SI system?

Answer: Kilogram meter squared ($\text{kg} \times \text{m}^2$). Derived from $[M][L]^2$ dimensional analysis.

Flashcard 12: 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 13: Determine the rotational inertia of a system of point masses.

Answer: $I = \text{sum of } m_i r_i^2$. Add up $mr^2$ for each individual mass element.

Flashcard 14: What is the effect of doubling radius on rotational inertia?

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

Flashcard 15: Calculate the rotational inertia of a composite object.

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

Flashcard 16: Which factor does rotational inertia depend on besides mass?

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

Flashcard 17: 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.

Flashcard 18: 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 19: What is the effect of doubling radius on rotational inertia?

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

Flashcard 20: 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 21: 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 22: How does increasing the radius affect rotational inertia?

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

Flashcard 23: 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 24: 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.

Flashcard 25: 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 26: 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 27: 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 28: Which factor does rotational inertia depend on besides mass?

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

Flashcard 29: What is the unit of rotational inertia in the SI system?

Answer: Kilogram meter squared ($\text{kg} \times \text{m}^2$). Derived from $[M][L]^2$ dimensional analysis.

Flashcard 30: What is the effect of mass distribution on rotational inertia?

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

Flashcard 31: 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 32: 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 33: 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 34: What is the relationship between torque and rotational inertia?

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

Flashcard 35: What is the effect of mass distribution on rotational inertia?

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

Flashcard 36: 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 37: What is the symbol for rotational inertia?

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

Flashcard 38: 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 39: State the formula for rotational inertia of a solid cylinder.

Answer: $I = \frac{1}{2} m r^2$. Standard formula for uniform solid cylinder about its axis.

Flashcard 40: 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 41: Determine the rotational inertia of a system of point masses.

Answer: $I = \text{sum of } m_i r_i^2$. Add up $mr^2$ for each individual mass element.

Flashcard 42: 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 43: 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 44: 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 45: 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 46: 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 47: Calculate the rotational inertia of a composite object.

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

Flashcard 48: What does the rotational inertia of an object signify?

Answer: Resistance to angular acceleration. Measures how hard it is to change angular motion.

Flashcard 49: How does increasing the radius affect rotational inertia?

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

Flashcard 50: 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 51: 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 52: What is the symbol for rotational inertia?

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

Flashcard 53: 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 54: 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 55: What does the rotational inertia of an object signify?

Answer: Resistance to angular acceleration. Measures how hard it is to change angular motion.

Flashcard 56: State the formula for rotational inertia of a solid cylinder.

Answer: $I = \frac{1}{2} m r^2$. Standard formula for uniform solid cylinder about its axis.

Flashcard 57: 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 58: 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 59: 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 60: 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 61: 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 62: 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.