Applications of circular motion
Section: Motion in a Circle | Syllabus: Cambridge AS Level Physics 9702
Banked Turns On high-speed tracks (velodromes or race circuits), bends are "banked" at an angle θ. This reduces reliance on friction. The normal force N provides a horizontal component toward the centre: N θ.
The vertical component supports the weight: N θ = mg. Condition for zero friction: θ = v^2/rg Diagram: Banked Track Forces Show a car on a slope of angle θ. Draw the Normal force N at an angle to the vertical.
Resolve N into N θ (vertical) and N θ (horizontal/centripetal). Vertical Circular Motion Unlike horizontal motion, gravity acts along the radius at the top and bottom, changing the net force. Force Analysis (Uniform Speed) At the Top (Point 1): Both T and W point down.
F_c = T + mg. At the Bottom (Point 3): T points up, W points down. F_c = T - mg T = F_c + mg. Conclusion: The string (or seat) must provide the maximum force at the bottom . This is where a string is most likely to break and where passengers feel "heaviest".
Minimum Speed at the Top To stay in a circle (e.g., water in a bucket), the weight mg must be less than or equal to the required centripetal force. v_ = √rg The Conical Pendulum A mass whirled in a horizontal circle by a string at an angle θ to the vertical.
T θ = F_c (Horizontal component provides rotation). T θ = mg (Vertical component supports weight). θ = v^2/rg Humps and Bridges When a car drives over a curved bridge of radius r, the weight acts toward the centre, and the normal force N acts outward.
F_c = mg - N N = mg - mv^2/r If the car goes too fast (v = √rg), the normal force N becomes zero, and the car leaves the road . Work Done in Circular Motion The work done by the centripetal force is always zero because the force is always perpendicular to the direction of motion (W = Fd 90^).
Therefore, the kinetic energy (and speed) of the object remains constant.
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