HSC Physics Harder Circular Motion

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A sheet of harder questions on circular motion follows.

  1. A railroad car is moving around a horizontal circular track. On which rail, the inner or the outer, does a greater force act on the wheels of the car?
  2. A railroad car is moving around a horizontal circular track of radius r with a speed v. The distance between the rails is d. If the height of the centre of gavity of the car above the rails is h, show that the ratio of the normal reaction reaction force exerted by the outer rail to the inner rail is (dgr + 2hv2)/(dgr - 2hv2).
  3. A thin ring of radius R and mass M rotates at an angular speed ⍵. Find the tension in the ring. (a) Why is the tension in the ring not zero? (b) Show that the tension in the ring is M R ⍵2/(2𝜋).