(a)Define the following terms;
(i)Angular velocity .
(ii)Torque.
(iii)Radius of gyration. (3 marks)
(b)(i) State the parallel axes theorem.(1 mark)
(ii)Show that the moment of inertia of a uniform rod of mass (m) and length(l) about an axis passing through its mid-length perpendicular to the rod is given by;
I= (Ml^2)/12
If the axis of rotation passes through to a point situated at ? th of the length of the rod, determine its moment of inertia using the parallel axis theorem.(2 marks)
(c)(i) Show that the moment of inertia of a solid disc of mass M and radius R about an axis through its centre and perpendicular to its plane is given by, (3 marks)
I=(MR^2)/2
(ii) A circular disc of radius 0.1m and mass 1 kg is rotating at a rate of 10 revolutions per second about its axis. Find the work that must be done to increase the rate of its revolution to 20 revolutions per second.(3 marks)
(iii)A uniform disc of mass 10 kg and radius 10 cm is mounted on a horizontal cylindrical axle of radius 2 cm and negligible mass. If a tangential force of 20N acts on the axle for 10 seconds from rest. Calculate:
Angular velocity acquired after 10 seconds.(2 marks)
Kinetic energy of the disc after 10 seconds. ( 1 mark)
Time taken to bring the disc to rest if a force of 2N is applied tangentially to the rim of the disc opposing its motion.(2 marks)
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