Rotational Kinematics - AP Physics 1
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Calculate the moment of inertia of a $2$ kg mass at $3$ m from the axis.
Calculate the moment of inertia of a $2$ kg mass at $3$ m from the axis.
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$I = 18$ kg·m². Use $I = mr^2$ with given mass and distance.
$I = 18$ kg·m². Use $I = mr^2$ with given mass and distance.
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What is the term for the rate of change of angular velocity?
What is the term for the rate of change of angular velocity?
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Angular Acceleration. The rate of change of angular velocity.
Angular Acceleration. The rate of change of angular velocity.
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Calculate the period of rotation for an object rotating at $5$ rad/s.
Calculate the period of rotation for an object rotating at $5$ rad/s.
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$T = \frac{2\text{π}}{5}$ s. Period equals $2\pi$ divided by angular velocity.
$T = \frac{2\text{π}}{5}$ s. Period equals $2\pi$ divided by angular velocity.
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State the relationship between linear velocity ($v$) and angular velocity ($\text{ω}$).
State the relationship between linear velocity ($v$) and angular velocity ($\text{ω}$).
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$v = r\text{ω}$. Linear velocity equals radius times angular velocity.
$v = r\text{ω}$. Linear velocity equals radius times angular velocity.
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State the equation of rotational kinetic energy.
State the equation of rotational kinetic energy.
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$K = \frac{1}{2}I\text{ω}^2$. Rotational analog of linear kinetic energy.
$K = \frac{1}{2}I\text{ω}^2$. Rotational analog of linear kinetic energy.
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What is the formula for rotational work done by a torque through an angle?
What is the formula for rotational work done by a torque through an angle?
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$W = \tau\theta$. Work done equals torque times angular displacement.
$W = \tau\theta$. Work done equals torque times angular displacement.
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What is the relationship between frequency ($f$) and period ($T$) of rotation?
What is the relationship between frequency ($f$) and period ($T$) of rotation?
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$f = \frac{1}{T}$. Frequency is the reciprocal of period.
$f = \frac{1}{T}$. Frequency is the reciprocal of period.
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What is the rotational analog of mass in linear motion?
What is the rotational analog of mass in linear motion?
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Moment of Inertia. Rotational inertia measures resistance to angular acceleration.
Moment of Inertia. Rotational inertia measures resistance to angular acceleration.
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State the relationship between torque and angular momentum change.
State the relationship between torque and angular momentum change.
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$\tau = \frac{dL}{dt}$. Torque equals the time rate of change of angular momentum.
$\tau = \frac{dL}{dt}$. Torque equals the time rate of change of angular momentum.
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Determine the torque if a $5$ N force is applied $0.5$ m from the pivot.
Determine the torque if a $5$ N force is applied $0.5$ m from the pivot.
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$\tau = 2.5$ N·m. Torque equals force times perpendicular distance.
$\tau = 2.5$ N·m. Torque equals force times perpendicular distance.
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What is the formula for the torque ($\tau$) acting on a rotating object?
What is the formula for the torque ($\tau$) acting on a rotating object?
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$\tau = rF\text{sin}(\theta)$. Torque depends on force, distance, and angle.
$\tau = rF\text{sin}(\theta)$. Torque depends on force, distance, and angle.
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Determine the frequency of a rotating object with a period of $0.5$ seconds.
Determine the frequency of a rotating object with a period of $0.5$ seconds.
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$f = 2$ Hz. Frequency equals one divided by period.
$f = 2$ Hz. Frequency equals one divided by period.
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Identify the formula relating tangential speed and angular speed.
Identify the formula relating tangential speed and angular speed.
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$v_{\text{tangential}} = r\text{ω}$. Tangential speed at distance $r$ from rotation axis.
$v_{\text{tangential}} = r\text{ω}$. Tangential speed at distance $r$ from rotation axis.
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Identify the formula for moment of inertia for a point mass.
Identify the formula for moment of inertia for a point mass.
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$I = mr^2$. Moment of inertia for a point mass at distance $r$.
$I = mr^2$. Moment of inertia for a point mass at distance $r$.
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Calculate the moment of inertia of a $2$ kg mass at $3$ m from the axis.
Calculate the moment of inertia of a $2$ kg mass at $3$ m from the axis.
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$I = 18$ kg·m². Use $I = mr^2$ with given mass and distance.
$I = 18$ kg·m². Use $I = mr^2$ with given mass and distance.
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Identify the formula for centripetal acceleration in terms of velocity and radius.
Identify the formula for centripetal acceleration in terms of velocity and radius.
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$a_c = \frac{v^2}{r}$. Acceleration directed toward the center of circular motion.
$a_c = \frac{v^2}{r}$. Acceleration directed toward the center of circular motion.
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State the relationship between linear displacement ($s$) and angular displacement ($\theta$).
State the relationship between linear displacement ($s$) and angular displacement ($\theta$).
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$s = r\theta$. Arc length equals radius times angular displacement.
$s = r\theta$. Arc length equals radius times angular displacement.
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Find the angular velocity if a wheel rotates $180$ degrees in $2$ seconds.
Find the angular velocity if a wheel rotates $180$ degrees in $2$ seconds.
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$\text{ω} = 1.57$ rad/s. Convert $180°$ to $\pi$ rad, then divide by time.
$\text{ω} = 1.57$ rad/s. Convert $180°$ to $\pi$ rad, then divide by time.
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Identify the formula for angular velocity in terms of angular displacement and time.
Identify the formula for angular velocity in terms of angular displacement and time.
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$\text{Angular velocity} = \frac{\theta}{t}$. Angular velocity equals angular displacement divided by time.
$\text{Angular velocity} = \frac{\theta}{t}$. Angular velocity equals angular displacement divided by time.
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Which principle relates torque to angular acceleration?
Which principle relates torque to angular acceleration?
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Newton's Second Law for Rotation. States that net torque equals $I\alpha$.
Newton's Second Law for Rotation. States that net torque equals $I\alpha$.
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What is the relationship between centripetal acceleration and angular velocity?
What is the relationship between centripetal acceleration and angular velocity?
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$a_c = r \omega^2$. Alternative form using angular velocity and radius.
$a_c = r \omega^2$. Alternative form using angular velocity and radius.
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State the formula for the centripetal force required for circular motion.
State the formula for the centripetal force required for circular motion.
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$F_c = \frac{mv^2}{r}$. Force needed to maintain circular motion.
$F_c = \frac{mv^2}{r}$. Force needed to maintain circular motion.
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State the formula for angular displacement in terms of initial and final angle.
State the formula for angular displacement in terms of initial and final angle.
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$\theta = \theta_f - \theta_i$. Angular displacement is the change in angular position.
$\theta = \theta_f - \theta_i$. Angular displacement is the change in angular position.
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Determine rotational kinetic energy of a $2$ kg·m² disk rotating at $4$ rad/s.
Determine rotational kinetic energy of a $2$ kg·m² disk rotating at $4$ rad/s.
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$K = 16$ J. Use $K = \frac{1}{2}I\omega^2$ formula.
$K = 16$ J. Use $K = \frac{1}{2}I\omega^2$ formula.
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Find the centripetal acceleration of a point on a wheel $0.2$ m from the center, rotating at $10$ rad/s.
Find the centripetal acceleration of a point on a wheel $0.2$ m from the center, rotating at $10$ rad/s.
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$a_c = 20$ m/s². Use $a_c = r\omega^2$ formula.
$a_c = 20$ m/s². Use $a_c = r\omega^2$ formula.
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State the unit of angular acceleration in the International System of Units (SI).
State the unit of angular acceleration in the International System of Units (SI).
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Radians per second squared (rad/s²). Standard SI unit for rotational acceleration.
Radians per second squared (rad/s²). Standard SI unit for rotational acceleration.
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Identify the angular displacement if a wheel turns $4$ revolutions.
Identify the angular displacement if a wheel turns $4$ revolutions.
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$\theta = 8\text{π}$ rad. One revolution equals $2\pi$ radians.
$\theta = 8\text{π}$ rad. One revolution equals $2\pi$ radians.
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Identify the conservation law applicable to a closed system with no external torques.
Identify the conservation law applicable to a closed system with no external torques.
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Conservation of Angular Momentum. Angular momentum remains constant without external torques.
Conservation of Angular Momentum. Angular momentum remains constant without external torques.
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What is the formula for angular momentum ($L$) of a rotating object?
What is the formula for angular momentum ($L$) of a rotating object?
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$L = I\text{ω}$. Angular momentum equals moment of inertia times angular velocity.
$L = I\text{ω}$. Angular momentum equals moment of inertia times angular velocity.
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What is the new angular velocity if a $2$ kg·m² object increases its moment of inertia to $4$ kg·m²?
What is the new angular velocity if a $2$ kg·m² object increases its moment of inertia to $4$ kg·m²?
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$\text{ω}{\text{new}} = \frac{1}{2}\text{ω}{\text{initial}}$. Conservation of angular momentum: $I_1\omega_1 = I_2\omega_2$.
$\text{ω}{\text{new}} = \frac{1}{2}\text{ω}{\text{initial}}$. Conservation of angular momentum: $I_1\omega_1 = I_2\omega_2$.
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