9231 · 3.3
Circular motion flashcards
Revision flashcards for Cambridge 9231 Circular motion (syllabus 3.3). Flip, recall, then mark a real past-paper question.
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What is angular velocity, ω?
The rate of change of angular displacement, measured in radians per second (rad s⁻¹). It is given by ω = dθ/dt.
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How are linear speed (v) and angular velocity (ω) related for a particle moving in a circle of radius r?
v = rω. The linear speed is the magnitude of the velocity vector, which is always tangential to the circle.
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What is centripetal acceleration?
The acceleration directed towards the centre of a circular path, responsible for changing the direction of the velocity vector. Its magnitude is a = v²/r = rω².
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What is centripetal force?
The net or resultant force directed towards the centre of a circular path that causes centripetal acceleration. It is given by F = mv²/r = mrω². It is NOT a fundamental force.
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A particle moves in a horizontal circle. What forces typically provide the centripetal force?
This depends on the situation. It could be the tension in a string (conical pendulum), the horizontal component of a normal reaction force (banked track), or friction.
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In a vertical circle problem, what is the condition for a particle on a string to complete the full circle?
The tension T must remain non-negative at all points. The critical point is the top of the circle, where tension is at its minimum. The condition is T_top ≥ 0, which implies the speed at the top, v_top, must satisfy v_top² ≥ gr.
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What is the condition for a particle to lose contact with the inside of a smooth spherical bowl?
The particle loses contact when the normal reaction force, R, becomes zero. You set R=0 in your radial force equation to find the angle or speed at which this occurs.
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For a car on a banked track of angle θ, what is the ideal speed 'v' to take the corner without relying on friction?
The speed at which the horizontal component of the normal reaction force provides the exact centripetal force required. The formula is tan(θ) = v² / (gr).
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Why is the work done by the centripetal force zero in uniform circular motion?
Because the centripetal force is always directed radially inwards, while the instantaneous displacement is always tangential. The force and displacement vectors are perpendicular, so the work done (W = F⋅d = Fd cos(90°)) is zero.
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What is transverse (or tangential) acceleration?
The component of acceleration tangent to the circular path. It is responsible for changing the speed of the particle. Its magnitude is a_t = r(dω/dt) = dv/dt. It is zero for uniform circular motion.