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: 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 2: 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 3: 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 4: 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 5: 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 6: 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 7: 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 8: 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 9: 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 10: 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 11: 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 12: 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 13: For rotational equilibrium, what must the net torque be?

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

Flashcard 14: 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 15: 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 16: 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 17: 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 18: What is the unit of torque in the SI system?

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

Flashcard 19: 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 20: What symbol represents angular acceleration?

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

Flashcard 21: 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 22: What condition must $\theta$ satisfy for maximum torque?

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

Flashcard 23: 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 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 rotational analog of mass in linear motion?

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

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 role of friction in rotational motion?

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

Flashcard 28: 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 29: 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 30: 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.