AP Physics 1 Flashcards: Newtons Second Law In Rotational Form

What this deck covers

This deck focuses on Newtons Second Law In Rotational Form, 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: How is rotational inertia affected by distance from rotation axis?

Answer: Increases with distance squared. Moment of inertia proportional to $r^2$ in $I = mr^2$.

Flashcard 2: What does the angle $\theta$ in the torque formula signify?

Answer: Angle between force vector and lever arm. Determines the component of force that creates rotation.

Flashcard 3: Calculate torque given $F = 10N$, $r = 2m$, and $\theta = 90^\circ$.

Answer: Torque = 20 Nm. Using $\tau = rF\sin\theta = (2)(10)(1) = 20$ Nm.

Flashcard 4: What happens to torque if the angle $\theta$ changes from $90^\circ$ to $0^\circ$?

Answer: Torque becomes zero. When $\theta = 0°$, $\sin\theta = 0$, so $\tau = 0$.

Flashcard 5: What is the effect on torque if force is applied perpendicular to lever arm?

Answer: Torque is maximized. Perpendicular force gives maximum torque since $\sin(90°) = 1$.

Flashcard 6: What does $r$ represent in the torque formula $\tau = rF\sin\theta$?

Answer: Lever arm length. Perpendicular distance from rotation axis to line of action of force.

Flashcard 7: What symbol represents angular acceleration?

Answer: $\alpha$. Greek letter alpha represents the rate of change of angular velocity.

Flashcard 8: How can torque be increased other than increasing force?

Answer: Increase lever arm length. Torque equals force times lever arm, so increase either factor.

Flashcard 9: What is the formula for net torque in terms of multiple forces?

Answer: $\tau_{net} = \sum (r_i F_i \sin\theta_i)$. Vector sum of individual torques from each applied force.

Flashcard 10: What is the rotational analog of Newton's first law?

Answer: An object in rotational equilibrium remains at rest or in uniform rotation. Objects maintain rotational state unless acted on by net torque.

Flashcard 11: What condition must $\theta$ satisfy for maximum torque?

Answer: $\theta = 90^\circ$. When force is perpendicular to lever arm, $\sin\theta = 1$.

Flashcard 12: What is the effect of increasing the lever arm on torque?

Answer: Torque increases. Torque is proportional to lever arm length in $\tau = rF\sin\theta$.

Flashcard 13: What does the symbol $I$ represent in rotational dynamics?

Answer: Moment of inertia. Rotational inertia - resistance to change in rotational motion.

Flashcard 14: What is the role of friction in rotational motion?

Answer: Can provide torque to change rotational motion. Friction forces can create torques about rotation axes.

Flashcard 15: What is the moment of inertia for a solid cylinder rotating about its central axis?

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

Flashcard 16: Determine angular acceleration if $\tau = 30 Nm$ and $I = 5 kg·m²$.

Answer: $\alpha = 6 \frac{rad}{s^2}$. Using $\alpha = \frac{\tau}{I} = \frac{30}{5} = 6$ rad/s².

Flashcard 17: What condition must $\theta$ satisfy for maximum torque?

Answer: $\theta = 90^\circ$. When force is perpendicular to lever arm, $\sin\theta = 1$.

Flashcard 18: What is the effect of reducing force to zero on angular acceleration?

Answer: Angular acceleration becomes zero. No torque means no angular acceleration from $\tau = I\alpha$.

Flashcard 19: If the moment of inertia is halved, what happens to angular acceleration?

Answer: Angular acceleration doubles. From $\alpha = \frac{\tau}{I}$, halving $I$ doubles $\alpha$.

Flashcard 20: What is the unit of torque in the SI system?

Answer: Newton meter (Nm). Force times distance units, equivalent to joules for torque.

Flashcard 21: What is Newton's Second Law in rotational form?

Answer: $\tau = I\alpha$. Rotational analog of $F = ma$, relating torque, inertia, and angular acceleration.

Flashcard 22: What happens to torque if the angle $\theta$ changes from $90^\circ$ to $0^\circ$?

Answer: Torque becomes zero. When $\theta = 0°$, $\sin\theta = 0$, so $\tau = 0$.

Flashcard 23: What is the relationship between net torque and rotational motion?

Answer: Net torque causes angular acceleration. Unbalanced torque produces change in rotational motion state.

Flashcard 24: What happens to angular acceleration if torque is doubled?

Answer: Angular acceleration doubles. From $\tau = I\alpha$, doubling $\tau$ doubles $\alpha$ when $I$ is constant.

Flashcard 25: What is the moment of inertia for a solid cylinder rotating about its central axis?

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

Flashcard 26: What does the angle $\theta$ in the torque formula signify?

Answer: Angle between force vector and lever arm. Determines the component of force that creates rotation.

Flashcard 27: What is the effect of increasing the moment of inertia on angular acceleration?

Answer: Angular acceleration decreases. From $\alpha = \frac{\tau}{I}$, larger $I$ means smaller $\alpha$.

Flashcard 28: Determine angular acceleration if $\tau = 30 Nm$ and $I = 5 kg·m²$.

Answer: $\alpha = 6 \frac{rad}{s^2}$. Using $\alpha = \frac{\tau}{I} = \frac{30}{5} = 6$ rad/s².

Flashcard 29: What is the rotational analog of mass in linear motion?

Answer: Moment of inertia ($I$). Measures resistance to rotational acceleration, like mass for linear motion.

Flashcard 30: What is the formula for net torque in terms of multiple forces?

Answer: $\tau_{net} = \sum (r_i F_i \sin\theta_i)$. Vector sum of individual torques from each applied force.

Flashcard 31: What is the moment of inertia for a solid sphere about its diameter?

Answer: $I = \frac{2}{5}mr^2$. Standard moment of inertia formula for uniform solid sphere.

Flashcard 32: If the moment of inertia is halved, what happens to angular acceleration?

Answer: Angular acceleration doubles. From $\alpha = \frac{\tau}{I}$, halving $I$ doubles $\alpha$.

Flashcard 33: What does the symbol $I$ represent in rotational dynamics?

Answer: Moment of inertia. Rotational inertia - resistance to change in rotational motion.

Flashcard 34: What is the relationship between net torque and rotational motion?

Answer: Net torque causes angular acceleration. Unbalanced torque produces change in rotational motion state.

Flashcard 35: What happens to angular acceleration if torque is doubled?

Answer: Angular acceleration doubles. From $\tau = I\alpha$, doubling $\tau$ doubles $\alpha$ when $I$ is constant.

Flashcard 36: What is the moment of inertia for a solid sphere about its diameter?

Answer: $I = \frac{2}{5}mr^2$. Standard moment of inertia formula for uniform solid sphere.

Flashcard 37: Calculate the moment of inertia for two masses, $m_1 = 2kg$ and $m_2 = 3kg$, at $r_1 = 1m$, $r_2 = 2m$.

Answer: $I = 2(1)^2 + 3(2)^2 = 14 kg·m²$. Sum individual contributions: $I = m_1r_1^2 + m_2r_2^2$.

Flashcard 38: How can torque be increased other than increasing force?

Answer: Increase lever arm length. Torque equals force times lever arm, so increase either factor.

Flashcard 39: What does $r$ represent in the torque formula $\tau = rF\sin\theta$?

Answer: Lever arm length. Perpendicular distance from rotation axis to line of action of force.

Flashcard 40: What is the effect of increasing the lever arm on torque?

Answer: Torque increases. Torque is proportional to lever arm length in $\tau = rF\sin\theta$.

Flashcard 41: What is the effect of mass distribution on moment of inertia?

Answer: Further mass increases moment of inertia. Mass farther from axis contributes more to rotational inertia.

Flashcard 42: What is the formula for the moment of inertia for a point mass?

Answer: $I = mr^2$. Mass times distance squared for a particle at distance $r$ from axis.

Flashcard 43: What is the moment of inertia for a thin hoop rotating about its central axis?

Answer: $I = mr^2$. All mass concentrated at radius $r$ from rotation axis.

Flashcard 44: What is the moment of inertia for a solid disk about an axis through its center?

Answer: $I = \frac{1}{2}mr^2$. Same as solid cylinder - uniform mass distribution about central axis.

Flashcard 45: What symbol represents angular acceleration?

Answer: $\alpha$. Greek letter alpha represents the rate of change of angular velocity.

Flashcard 46: Identify the unit of moment of inertia in the SI system.

Answer: Kilogram meter squared (kg·m²). Mass times distance squared units from rotational inertia definition.

Flashcard 47: What is Newton's Second Law in rotational form?

Answer: $\tau = I\alpha$. Rotational analog of $F = ma$, relating torque, inertia, and angular acceleration.

Flashcard 48: What is the formula for the moment of inertia for a point mass?

Answer: $I = mr^2$. Mass times distance squared for a particle at distance $r$ from axis.

Flashcard 49: What is the effect of balanced torques on an object?

Answer: The object is in rotational equilibrium. Equal and opposite torques cancel, producing no angular acceleration.

Flashcard 50: What is the rotational analog of Newton's first law?

Answer: An object in rotational equilibrium remains at rest or in uniform rotation. Objects maintain rotational state unless acted on by net torque.

Flashcard 51: Define torque in the context of rotational motion.

Answer: Torque ($\tau$) is the rotational equivalent of force. It causes angular acceleration just like force causes linear acceleration.

Flashcard 52: What does a non-zero net torque indicate about an object's motion?

Answer: The object is undergoing angular acceleration. Net torque causes change in angular velocity over time.

Flashcard 53: How is angular acceleration calculated from torque and moment of inertia?

Answer: $\alpha = \frac{\tau}{I}$. Derived from rearranging Newton's second law for rotation.

Flashcard 54: What is the moment of inertia for a thin hoop rotating about its central axis?

Answer: $I = mr^2$. All mass concentrated at radius $r$ from rotation axis.

Flashcard 55: Identify the relationship between torque and angular acceleration.

Answer: Directly proportional. Greater torque produces greater angular acceleration when $I$ is constant.

Flashcard 56: For rotational equilibrium, what must the net torque be?

Answer: Zero. No net torque means no angular acceleration occurs.

Flashcard 57: What is the formula for torque involving force and lever arm?

Answer: $\tau = rF\sin\theta$. Torque equals perpendicular force component times lever arm distance.

Flashcard 58: What is the formula for torque involving force and lever arm?

Answer: $\tau = rF\sin\theta$. Torque equals perpendicular force component times lever arm distance.

Flashcard 59: Identify the unit of moment of inertia in the SI system.

Answer: Kilogram meter squared (kg·m²). Mass times distance squared units from rotational inertia definition.

Flashcard 60: Calculate the moment of inertia for two masses, $m_1 = 2kg$ and $m_2 = 3kg$, at $r_1 = 1m$, $r_2 = 2m$.

Answer: $I = 2(1)^2 + 3(2)^2 = 14 kg·m²$. Sum individual contributions: $I = m_1r_1^2 + m_2r_2^2$.

Flashcard 61: What is the rotational analog of mass in linear motion?

Answer: Moment of inertia ($I$). Measures resistance to rotational acceleration, like mass for linear motion.

Flashcard 62: Define torque in the context of rotational motion.

Answer: Torque ($\tau$) is the rotational equivalent of force. It causes angular acceleration just like force causes linear acceleration.

Flashcard 63: What is the effect on torque if force is applied perpendicular to lever arm?

Answer: Torque is maximized. Perpendicular force gives maximum torque since $\sin(90°) = 1$.

Flashcard 64: What is the moment of inertia for a solid disk about an axis through its center?

Answer: $I = \frac{1}{2}mr^2$. Same as solid cylinder - uniform mass distribution about central axis.

Flashcard 65: What does a non-zero net torque indicate about an object's motion?

Answer: The object is undergoing angular acceleration. Net torque causes change in angular velocity over time.

Flashcard 66: What is the effect of mass distribution on moment of inertia?

Answer: Further mass increases moment of inertia. Mass farther from axis contributes more to rotational inertia.

Flashcard 67: What is the effect of increasing the moment of inertia on angular acceleration?

Answer: Angular acceleration decreases. From $\alpha = \frac{\tau}{I}$, larger $I$ means smaller $\alpha$.

Flashcard 68: How is rotational inertia affected by distance from rotation axis?

Answer: Increases with distance squared. Moment of inertia proportional to $r^2$ in $I = mr^2$.

Flashcard 69: What is the effect of balanced torques on an object?

Answer: The object is in rotational equilibrium. Equal and opposite torques cancel, producing no angular acceleration.

Flashcard 70: How is angular acceleration calculated from torque and moment of inertia?

Answer: $\alpha = \frac{\tau}{I}$. Derived from rearranging Newton's second law for rotation.

Flashcard 71: Identify the relationship between torque and angular acceleration.

Answer: Directly proportional. Greater torque produces greater angular acceleration when $I$ is constant.

Flashcard 72: What is the role of friction in rotational motion?

Answer: Can provide torque to change rotational motion. Friction forces can create torques about rotation axes.

Flashcard 73: What is the unit of torque in the SI system?

Answer: Newton meter (Nm). Force times distance units, equivalent to joules for torque.

Flashcard 74: For rotational equilibrium, what must the net torque be?

Answer: Zero. No net torque means no angular acceleration occurs.