Connecting Linear and Rotational Motion - AP Physics 1
Card 1 of 29
Calculate the centripetal acceleration for $v = 5 \text{ m/s}$ and $r = 2 \text{ m}$.
Calculate the centripetal acceleration for $v = 5 \text{ m/s}$ and $r = 2 \text{ m}$.
Tap to reveal answer
$a_c = 12.5 \text{ m/s}^2$. Apply $a_c = v^2/r$: $a_c = 5^2/2 = 12.5 \text{ m/s}^2$.
$a_c = 12.5 \text{ m/s}^2$. Apply $a_c = v^2/r$: $a_c = 5^2/2 = 12.5 \text{ m/s}^2$.
← Didn't Know|Knew It →
Find the angular acceleration if the tangential acceleration is $8 \text{ m/s}^2$ and the radius is $4 \text{ m}$.
Find the angular acceleration if the tangential acceleration is $8 \text{ m/s}^2$ and the radius is $4 \text{ m}$.
Tap to reveal answer
$\beta = 2 \text{ rad/s}^2$. Apply $\alpha = a_t/r$: $\alpha = 8/4 = 2 \text{ rad/s}^2$.
$\beta = 2 \text{ rad/s}^2$. Apply $\alpha = a_t/r$: $\alpha = 8/4 = 2 \text{ rad/s}^2$.
← Didn't Know|Knew It →
Find the linear velocity for an object rotating at $\theta = 4 \text{ rad/s}$ with radius $r = 0.5 \text{ m}$.
Find the linear velocity for an object rotating at $\theta = 4 \text{ rad/s}$ with radius $r = 0.5 \text{ m}$.
Tap to reveal answer
$v = 2 \text{ m/s}$. Apply $v = r\omega$: $v = 0.5 \times 4 = 2$ m/s.
$v = 2 \text{ m/s}$. Apply $v = r\omega$: $v = 0.5 \times 4 = 2$ m/s.
← Didn't Know|Knew It →
State the equation for the work done by torque over an angular displacement.
State the equation for the work done by torque over an angular displacement.
Tap to reveal answer
$W = \tau \times \theta$. Rotational work equals torque times angular displacement.
$W = \tau \times \theta$. Rotational work equals torque times angular displacement.
← Didn't Know|Knew It →
What is the linear distance traveled by a point on the rim of a wheel with radius $r$ after one revolution?
What is the linear distance traveled by a point on the rim of a wheel with radius $r$ after one revolution?
Tap to reveal answer
$d = 2\text{π}r$. Circumference of circle with radius $r$.
$d = 2\text{π}r$. Circumference of circle with radius $r$.
← Didn't Know|Knew It →
Find the angular momentum for $I = 8 \text{ kg m}^2$ and $\theta = 3 \text{ rad/s}$.
Find the angular momentum for $I = 8 \text{ kg m}^2$ and $\theta = 3 \text{ rad/s}$.
Tap to reveal answer
$L = 24 \text{ kg m}^2/\text{s}$. Apply $L = I\omega$: $L = 8 \times 3 = 24$ kg⋅m²/s.
$L = 24 \text{ kg m}^2/\text{s}$. Apply $L = I\omega$: $L = 8 \times 3 = 24$ kg⋅m²/s.
← Didn't Know|Knew It →
Identify the unit for moment of inertia.
Identify the unit for moment of inertia.
Tap to reveal answer
Kilogram meter squared (kg m$^2$). SI unit for moment of inertia.
Kilogram meter squared (kg m$^2$). SI unit for moment of inertia.
← Didn't Know|Knew It →
Calculate the angular velocity for a wheel with $v = 10 \text{ m/s}$ and $r = 2 \text{ m}$.
Calculate the angular velocity for a wheel with $v = 10 \text{ m/s}$ and $r = 2 \text{ m}$.
Tap to reveal answer
$\theta = 5 \text{ rad/s}$. Apply $\omega = v/r$: $\omega = 10/2 = 5 \text{ rad/s}$
$\theta = 5 \text{ rad/s}$. Apply $\omega = v/r$: $\omega = 10/2 = 5 \text{ rad/s}$
← Didn't Know|Knew It →
What is the formula for angular momentum in terms of mass, velocity, and radius?
What is the formula for angular momentum in terms of mass, velocity, and radius?
Tap to reveal answer
$L = mvr$. Angular momentum for linear motion in circular path.
$L = mvr$. Angular momentum for linear motion in circular path.
← Didn't Know|Knew It →
Convert an angular velocity of $3 \text{ rad/s}$ to linear velocity if $r = 2 \text{ m}$.
Convert an angular velocity of $3 \text{ rad/s}$ to linear velocity if $r = 2 \text{ m}$.
Tap to reveal answer
$v = 6 \text{ m/s}$. Apply $v = r\omega$: $v = 2 \times 3 = 6$ m/s.
$v = 6 \text{ m/s}$. Apply $v = r\omega$: $v = 2 \times 3 = 6$ m/s.
← Didn't Know|Knew It →
Calculate the torque for a force of $10 \text{ N}$ applied at $2 \text{ m}$ from the pivot.
Calculate the torque for a force of $10 \text{ N}$ applied at $2 \text{ m}$ from the pivot.
Tap to reveal answer
$\tau = 20 \text{ Nm}$. Apply $\tau = rF$: $\tau = 2 \times 10 = 20$ Nm.
$\tau = 20 \text{ Nm}$. Apply $\tau = rF$: $\tau = 2 \times 10 = 20$ Nm.
← Didn't Know|Knew It →
Calculate the moment of inertia for a hoop with mass $m = 5 \text{ kg}$ and radius $r = 1 \text{ m}$.
Calculate the moment of inertia for a hoop with mass $m = 5 \text{ kg}$ and radius $r = 1 \text{ m}$.
Tap to reveal answer
$I = 5 \text{ kg m}^2$. For a hoop, $I = mr^2$: $I = 5 \times 1^2 = 5$ kg⋅m².
$I = 5 \text{ kg m}^2$. For a hoop, $I = mr^2$: $I = 5 \times 1^2 = 5$ kg⋅m².
← Didn't Know|Knew It →
Calculate the angular momentum for a point mass with mass $m = 2 \text{ kg}$, radius $r = 3 \text{ m}$, and velocity $v = 4 \text{ m/s}$.
Calculate the angular momentum for a point mass with mass $m = 2 \text{ kg}$, radius $r = 3 \text{ m}$, and velocity $v = 4 \text{ m/s}$.
Tap to reveal answer
$L = 24 \text{ kg m}^2/\text{s}$. Apply $L = mvr$: $L = 2 \times 4 \times 3 = 24$ kg⋅m²/s.
$L = 24 \text{ kg m}^2/\text{s}$. Apply $L = mvr$: $L = 2 \times 4 \times 3 = 24$ kg⋅m²/s.
← Didn't Know|Knew It →
What is the unit of angular velocity?
What is the unit of angular velocity?
Tap to reveal answer
Radians per second (rad/s). Standard SI unit for angular velocity measurement.
Radians per second (rad/s). Standard SI unit for angular velocity measurement.
← Didn't Know|Knew It →
What is the relationship between work done and torque in rotational motion?
What is the relationship between work done and torque in rotational motion?
Tap to reveal answer
$W = \tau \times \theta$. Work done equals torque times angular displacement.
$W = \tau \times \theta$. Work done equals torque times angular displacement.
← Didn't Know|Knew It →
Calculate the rotational kinetic energy of a disc with $I = 2 \text{ kg m}^2$ and $\theta = 3 \text{ rad/s}$.
Calculate the rotational kinetic energy of a disc with $I = 2 \text{ kg m}^2$ and $\theta = 3 \text{ rad/s}$.
Tap to reveal answer
$KE_{rot} = 9 \text{ J}$. Apply $KE = \frac{1}{2}I\omega^2$: $KE = \frac{1}{2} \times 2 \times 3^2 = 9$ J.
$KE_{rot} = 9 \text{ J}$. Apply $KE = \frac{1}{2}I\omega^2$: $KE = \frac{1}{2} \times 2 \times 3^2 = 9$ J.
← Didn't Know|Knew It →
Identify the unit of torque.
Identify the unit of torque.
Tap to reveal answer
Newton meter (Nm). SI unit for torque measurement.
Newton meter (Nm). SI unit for torque measurement.
← Didn't Know|Knew It →
State the formula for torque in terms of force and radius.
State the formula for torque in terms of force and radius.
Tap to reveal answer
$\tau = r \times F$. Torque equals force times perpendicular distance from pivot.
$\tau = r \times F$. Torque equals force times perpendicular distance from pivot.
← Didn't Know|Knew It →
What is the formula for the total acceleration of a point on a rotating body?
What is the formula for the total acceleration of a point on a rotating body?
Tap to reveal answer
$a_{total} = \text{√}(a_t^2 + a_c^2)$. Pythagorean sum of tangential and centripetal accelerations.
$a_{total} = \text{√}(a_t^2 + a_c^2)$. Pythagorean sum of tangential and centripetal accelerations.
← Didn't Know|Knew It →
What is the relationship between linear displacement and angular displacement?
What is the relationship between linear displacement and angular displacement?
Tap to reveal answer
$s = r \times \theta$. Arc length equals radius times angle in radians.
$s = r \times \theta$. Arc length equals radius times angle in radians.
← Didn't Know|Knew It →
Calculate the tangential acceleration for $\beta = 5 \text{ rad/s}^2$ and $r = 0.3 \text{ m}$.
Calculate the tangential acceleration for $\beta = 5 \text{ rad/s}^2$ and $r = 0.3 \text{ m}$.
Tap to reveal answer
$a_t = 1.5 \text{ m/s}^2$. Apply $a_t = r\alpha$: $a_t = 0.3 \times 5 = 1.5 \text{ m/s}^2$.
$a_t = 1.5 \text{ m/s}^2$. Apply $a_t = r\alpha$: $a_t = 0.3 \times 5 = 1.5 \text{ m/s}^2$.
← Didn't Know|Knew It →
What is the moment of inertia for a solid cylinder about its central axis?
What is the moment of inertia for a solid cylinder about its central axis?
Tap to reveal answer
$I = \frac{1}{2} m \times r^2$. Standard formula for solid cylinder rotating about its axis.
$I = \frac{1}{2} m \times r^2$. Standard formula for solid cylinder rotating about its axis.
← Didn't Know|Knew It →
What is the formula for the centripetal acceleration in terms of linear velocity and radius?
What is the formula for the centripetal acceleration in terms of linear velocity and radius?
Tap to reveal answer
$a_c = \frac{v^2}{r}$. Standard formula for centripetal acceleration.
$a_c = \frac{v^2}{r}$. Standard formula for centripetal acceleration.
← Didn't Know|Knew It →
What is the equation for the moment of inertia of a point mass?
What is the equation for the moment of inertia of a point mass?
Tap to reveal answer
$I = m \times r^2$. For a point mass at distance $r$ from the axis.
$I = m \times r^2$. For a point mass at distance $r$ from the axis.
← Didn't Know|Knew It →
Convert a linear velocity of $5 \text{ m/s}$ to angular velocity for $r = 0.5 \text{ m}$.
Convert a linear velocity of $5 \text{ m/s}$ to angular velocity for $r = 0.5 \text{ m}$.
Tap to reveal answer
$\theta = 10 \text{ rad/s}$. Apply $\omega = v/r$: $\omega = 5/0.5 = 10$ rad/s.
$\theta = 10 \text{ rad/s}$. Apply $\omega = v/r$: $\omega = 5/0.5 = 10$ rad/s.
← Didn't Know|Knew It →
What is the moment of inertia for a solid cylinder about its central axis?
What is the moment of inertia for a solid cylinder about its central axis?
Tap to reveal answer
$I = \frac{1}{2} m \times r^2$. Standard formula for solid cylinder rotating about its axis.
$I = \frac{1}{2} m \times r^2$. Standard formula for solid cylinder rotating about its axis.
← Didn't Know|Knew It →
Calculate the centripetal acceleration for $v = 5 \text{ m/s}$ and $r = 2 \text{ m}$.
Calculate the centripetal acceleration for $v = 5 \text{ m/s}$ and $r = 2 \text{ m}$.
Tap to reveal answer
$a_c = 12.5 \text{ m/s}^2$. Apply $a_c = v^2/r$: $a_c = 5^2/2 = 12.5 \text{ m/s}^2$.
$a_c = 12.5 \text{ m/s}^2$. Apply $a_c = v^2/r$: $a_c = 5^2/2 = 12.5 \text{ m/s}^2$.
← Didn't Know|Knew It →
What is the formula for the centripetal acceleration in terms of linear velocity and radius?
What is the formula for the centripetal acceleration in terms of linear velocity and radius?
Tap to reveal answer
$a_c = \frac{v^2}{r}$. Standard formula for centripetal acceleration.
$a_c = \frac{v^2}{r}$. Standard formula for centripetal acceleration.
← Didn't Know|Knew It →
Convert an angular velocity of $3 \text{ rad/s}$ to linear velocity if $r = 2 \text{ m}$.
Convert an angular velocity of $3 \text{ rad/s}$ to linear velocity if $r = 2 \text{ m}$.
Tap to reveal answer
$v = 6 \text{ m/s}$. Apply $v = r\omega$: $v = 2 \times 3 = 6$ m/s.
$v = 6 \text{ m/s}$. Apply $v = r\omega$: $v = 2 \times 3 = 6$ m/s.
← Didn't Know|Knew It →