Rotational Equilibrium and Newton's First Law - AP Physics 1
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What happens to torque if the angle $\theta = 0^\text{o}$?
What happens to torque if the angle $\theta = 0^\text{o}$?
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Torque is zero. Force parallel to radius produces no rotation.
Torque is zero. Force parallel to radius produces no rotation.
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Which direction does positive torque rotate an object?
Which direction does positive torque rotate an object?
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Counterclockwise. Standard convention for positive rotation.
Counterclockwise. Standard convention for positive rotation.
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What is the condition for rotational equilibrium?
What is the condition for rotational equilibrium?
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Net torque ($\tau_{\text{net}}$) must be zero. No angular acceleration occurs when forces balance.
Net torque ($\tau_{\text{net}}$) must be zero. No angular acceleration occurs when forces balance.
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Identify the variable representing angular displacement.
Identify the variable representing angular displacement.
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$\theta$. Symbol for angular position measurement.
$\theta$. Symbol for angular position measurement.
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Find the torque if $r = 3 \text{m}$, $F = 4 \text{N}$, $\theta = 90^\text{o}$.
Find the torque if $r = 3 \text{m}$, $F = 4 \text{N}$, $\theta = 90^\text{o}$.
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$\tau = 12 \text{N·m}$. $\tau = 3 \times 4 \times \sin(90°) = 12$.
$\tau = 12 \text{N·m}$. $\tau = 3 \times 4 \times \sin(90°) = 12$.
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State the formula for moment of inertia of a point mass.
State the formula for moment of inertia of a point mass.
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$I = m \times r^2$. Mass times distance squared from axis.
$I = m \times r^2$. Mass times distance squared from axis.
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What is the condition for an object to be in static rotational equilibrium?
What is the condition for an object to be in static rotational equilibrium?
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Net torque and net force must both be zero. No linear or rotational acceleration.
Net torque and net force must both be zero. No linear or rotational acceleration.
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Which direction does negative torque rotate an object?
Which direction does negative torque rotate an object?
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Clockwise. Standard convention for negative rotation.
Clockwise. Standard convention for negative rotation.
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If $\tau = 0$, what can be inferred about the object's rotation?
If $\tau = 0$, what can be inferred about the object's rotation?
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The object is either at rest or in uniform rotation. Newton's first law for rotation applies.
The object is either at rest or in uniform rotation. Newton's first law for rotation applies.
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State the condition for equilibrium of a rotational system.
State the condition for equilibrium of a rotational system.
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Sum of all external torques must be zero. Rotational equilibrium requires balanced torques.
Sum of all external torques must be zero. Rotational equilibrium requires balanced torques.
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What is the effect of torque on an object's rotational state?
What is the effect of torque on an object's rotational state?
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Changes the object's angular velocity. Torque causes rotational acceleration or deceleration.
Changes the object's angular velocity. Torque causes rotational acceleration or deceleration.
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Identify the direction of the torque vector.
Identify the direction of the torque vector.
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Perpendicular to the plane formed by $r$ and $F$. Right-hand rule determines direction.
Perpendicular to the plane formed by $r$ and $F$. Right-hand rule determines direction.
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What is the condition for equilibrium of a seesaw?
What is the condition for equilibrium of a seesaw?
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Sum of clockwise torques = Sum of counterclockwise torques. Torques must balance for equilibrium.
Sum of clockwise torques = Sum of counterclockwise torques. Torques must balance for equilibrium.
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Find the net torque if $\tau_1 = 5 \text{N·m}$ and $\tau_2 = -3 \text{N·m}$.
Find the net torque if $\tau_1 = 5 \text{N·m}$ and $\tau_2 = -3 \text{N·m}$.
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Net torque = $2 \text{N·m}$. Vector sum: $5 + (-3) = 2$.
Net torque = $2 \text{N·m}$. Vector sum: $5 + (-3) = 2$.
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What is the relationship between torque and rotational inertia?
What is the relationship between torque and rotational inertia?
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Torque causes rotational inertia to change angular velocity. Torque overcomes inertia to change motion.
Torque causes rotational inertia to change angular velocity. Torque overcomes inertia to change motion.
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Identify the symbol for angular velocity.
Identify the symbol for angular velocity.
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$\text{omega} (\text{ω})$. Greek letter representing angular velocity.
$\text{omega} (\text{ω})$. Greek letter representing angular velocity.
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What happens to an object in rotational equilibrium if external torque is applied?
What happens to an object in rotational equilibrium if external torque is applied?
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It will begin to rotate. Equilibrium breaks, causing angular acceleration.
It will begin to rotate. Equilibrium breaks, causing angular acceleration.
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What is the rotational analog of force in linear motion?
What is the rotational analog of force in linear motion?
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Torque ($\tau$). Rotational equivalent of linear force.
Torque ($\tau$). Rotational equivalent of linear force.
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What is the rotational analog of mass?
What is the rotational analog of mass?
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Moment of inertia ($I$). Resistance to rotational motion.
Moment of inertia ($I$). Resistance to rotational motion.
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State the formula for angular velocity.
State the formula for angular velocity.
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$\text{Angular velocity} (\text{rad/s}) = \frac{\text{Change in angle}}{\text{Change in time}}$. Rate of angular position change.
$\text{Angular velocity} (\text{rad/s}) = \frac{\text{Change in angle}}{\text{Change in time}}$. Rate of angular position change.
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Find the angular acceleration if $I = 2 \text{kg·m}^2$ and $\tau = 4 \text{N·m}$.
Find the angular acceleration if $I = 2 \text{kg·m}^2$ and $\tau = 4 \text{N·m}$.
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$\text{α} = 2 \text{rad/s}^2$. Using $\alpha = \tau/I = 4/2 = 2$.
$\text{α} = 2 \text{rad/s}^2$. Using $\alpha = \tau/I = 4/2 = 2$.
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State Newton's First Law in rotational form.
State Newton's First Law in rotational form.
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An object remains at rest or in uniform rotation unless acted upon by a net external torque. Rotational version of inertia law.
An object remains at rest or in uniform rotation unless acted upon by a net external torque. Rotational version of inertia law.
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What is the formula for angular acceleration?
What is the formula for angular acceleration?
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$\text{Angular acceleration} (\text{α}) = \frac{\text{Change in angular velocity}}{\text{Change in time}}$. Rate of angular velocity change.
$\text{Angular acceleration} (\text{α}) = \frac{\text{Change in angular velocity}}{\text{Change in time}}$. Rate of angular velocity change.
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How does increasing the force $F$ affect the torque?
How does increasing the force $F$ affect the torque?
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Increases torque, if $r$ and $\theta$ remain constant. Torque is proportional to applied force.
Increases torque, if $r$ and $\theta$ remain constant. Torque is proportional to applied force.
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Identify the unit of torque in SI units.
Identify the unit of torque in SI units.
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Newton-meter (N·m). Force times distance unit.
Newton-meter (N·m). Force times distance unit.
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What is the significance of the angle $\theta$ in torque calculations?
What is the significance of the angle $\theta$ in torque calculations?
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Determines the component of force causing rotation. Only perpendicular force component creates torque.
Determines the component of force causing rotation. Only perpendicular force component creates torque.
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What is torque's formula?
What is torque's formula?
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$\tau = r \times F \times \text{sin}(\theta)$. Force times perpendicular distance from axis.
$\tau = r \times F \times \text{sin}(\theta)$. Force times perpendicular distance from axis.
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What is the rotational kinetic energy formula?
What is the rotational kinetic energy formula?
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$KE_{\text{rotational}} = \frac{1}{2} I \times \text{ω}^2$. Rotational analog of $\frac{1}{2}mv^2$.
$KE_{\text{rotational}} = \frac{1}{2} I \times \text{ω}^2$. Rotational analog of $\frac{1}{2}mv^2$.
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Which quantity remains constant for an object in rotational equilibrium?
Which quantity remains constant for an object in rotational equilibrium?
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Angular velocity remains constant. No net torque means constant rotation.
Angular velocity remains constant. No net torque means constant rotation.
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What happens to angular velocity if net torque is applied?
What happens to angular velocity if net torque is applied?
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Angular velocity changes. Net torque causes angular acceleration.
Angular velocity changes. Net torque causes angular acceleration.
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