IB Physics. Centripetal Force

A tutorial sheet on centripetal force follows.

1. The Earth rotates on its axis once every 23 h 56 m 4 s. Why do objects remain at rest on the Earth (relative to the Earth) ?
2. Imagine that the Earth's period of rotation is 2 h. Would an object on the Earth stay at rest on the Earth? Explain.
3. A planet of mass M has a radius R and has a period of rotation about its axis of T. Find the weight, relative to the surface of the planet, of a mass m at latitude θ on the planet.
4. A centrifuge is spinning at a rate ω. Do heavier particles accumulate near the centre or the outside? Explain.
5. A mass m can slide on a smooth horizontal rod. The mass is placed at the centre of the rod. The rod rotates with a constant angular speed ω about an axis perpendicular to one end. Does the mass stay at rest relative to the rod, move inwards or outwards? Explain.

IB Physics. Motion in a Vertical Circle

A sheet of harder questions on a mass moving on a string in a vertical circle is given below.

1. A mass m hangs at rest on the end of a light inextensible string of length L. The mass is given a horizontal velocity U and the maximum vertical height to which the mass rises is L. Find U.
2. In the previous question find the tension in the string and the magnitude of the acceleration of the mass at its highest point.
3. A mass m is on the end of a string of length L that has its upper end fixed. The mass is released from rest and swings in a circular arc. Find an expression for the tension in the string when the string makes an angle 𝜃 with the vertical.
4. A mass hangs at rest on the end of a light inextensible string of length L. The mass is given a horizontal speed U. In its subsequent motion the string becomes slack and the mass hits the point of supprt of the string. Find the initial speed U.