he formula for rotational kinetic energy?","back":"$$E_k = \\frac{1}{2} I \\omega^2$","points":1,"mcqOptions":[{"text":"$$E_k = \\frac{1}{2} I \\omega^2$","correct":true,"explanation":"Rotational kinetic energy depends on the moment of inertia and the square of angular speed, directly paralleling translational kinetic energy, $E_k = \\frac{1}{2}mv^2$."},{"text":"$$E_k = \\frac{1}{2} I \\omega$","correct":false,"explanation":"This omits the square on angular speed. As in the linear kinetic energy formula, speed must be squared, giving $E_k = \\frac{1}{2}I\\omega^2$."},{"text":"$$E_k = I \\omega^2$","correct":false,"explanation":"This misses the factor of one-half, making the calculated energy twice its correct value. The rotational kinetic energy is $E_k = \\frac{1}{2}I\\omega^2$."},{"text":"$$E_k = \\frac{1}{2} I^2 \\omega$","correct":false,"explanation":"This incorrectly squares the moment of inertia instead of angular speed. Rotational kinetic energy is proportional to $I$ and to $\\omega^2$, so $E_k = \\frac{1}{2}I\\omega^2$."}]},{"id":"ac121981-79e6-41ae-a925-c04cd31fa90d","cardType":"basic","front":"Which two rotational variables replace mass and linear velocity in the kinetic energy formula?","back":"

Moment of inertia ($I$)
Angular speed ($\\omega$)

","points":2,"mcqOptions":[{"text":"

Moment of inertia ($I$)
Angular speed ($\\omega$)

","correct":true,"explanation":"Moment of inertia is the rotational equivalent of mass, while angular speed is the rotational equivalent of linear velocity. Substituting them gives $E_k = \\frac{1}{2}I\\omega^2$."},{"text":"

Moment of inertia ($I$)
Angular acceleration ($\\alpha$)

","correct":false,"explanation":"Angular acceleration corresponds to linear acceleration, not linear velocity. The kinetic energy formula replaces mass with moment of inertia and linear velocity with angular speed."},{"text":"

Torque ($\\tau$)
Angular speed ($\\omega$)

","correct":false,"explanation":"Torque is the rotational equivalent of force rather than mass. Mass is replaced by moment of inertia, while linear velocity is replaced by angular speed."},{"text":"

Angular momentum ($L$)
Angular acceleration ($\\alpha$)

","correct":false,"explanation":"Angular momentum is analogous to linear momentum, and angular acceleration corresponds to linear acceleration. Rotational kinetic energy instead uses moment of inertia and angular speed."}]}]}],"examCountdown":{"examDate":"2027-05-21","paperLabel":"Paper 1"},"heading":"Rotational kinetic energy (A-level only)","title":"Rotational kinetic energy (A-level only) Flashcards","topicSidebar":"$L41"}]}],"topicId":"69f4f22e-a8b5-58aa-9468-d624143d880a","walled":"$L42"}],"$L43"]