Flashcards · 9702 · A Level Topic 12

Motion in a circle (A Level) flashcards

11 cards on A Level Topic 12, subtopics 12.1 to 12.2. Pick a subtopic or study them all.

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The radian: The angle subtended at the centre of a circle by an arc equal in length to the radius. Angle in radians = arc length ÷ radius.
Converting between degrees and radians: 360° = 2π rad, so θ (rad) = θ (degrees) × π ÷ 180. 1 rad ≈ 57.3°.
Angular speed: The rate of change of angle swept out: ω = θ ÷ t = 2π ÷ T = 2πf. Unit rad s⁻¹.
Relationship between linear speed and angular speed: v = rω, with ω in rad s⁻¹.
A wheel of radius 0.30 m turns at 5.0 revolutions per second. Find ω and the rim speed.: ω = 2π × 5.0 = 31.4 rad s⁻¹. v = rω = 0.30 × 31.4 = 9.4 m s⁻¹.

Why is an object moving in a circle at constant speed accelerating?: Its direction keeps changing, so its velocity (a vector) changes even though its speed is constant.
Centripetal acceleration and force: a = v² ÷ r = rω². F = mv² ÷ r = mrω². Both are directed towards the centre of the circle.
Is centripetal force an extra force on a free-body diagram?: No. It is the resultant of the real forces acting, for example tension (ball on a string), friction (car on a flat bend) or gravity (planet in orbit).
Why does a centripetal force do no work?: It is perpendicular to the velocity at every instant, so there is no displacement along it. The kinetic energy stays constant.
Minimum speed at the top of a vertical circle (mass on a string): At minimum speed the tension is zero and weight alone provides the centripetal force: mg = mv² ÷ r, so v = √(gr).
Tension at the top and bottom of a vertical circle: Top: T + mg = mv² ÷ r. Bottom: T − mg = mv² ÷ r. The tension is greatest at the bottom.