(a) A child stands at the centre of a turntable with his two arms outstretched. The
turntable is set rotating with an angular speed of 40 rev/min. How much is the
angular speed of the child if he folds his hands back and thereby reduces his
moment of inertia to 2/5 times the initial value ? Assume that the turntable
rotates without friction.
(b) Show that the child’s new kinetic energy of rotation is more than the initial
kinetic energy of rotation. How do you account for this increase in kinetic energy?
A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s-1.
The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the
rotation of the cylinder? What is the magnitude of angular momentum of the cylinder
about its axis?
Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both
having the same mass and radius. The cylinder is free to rotate about its standard
axis of symmetry, and the sphere is free to rotate about an axis passing through its
centre. Which of the two will acquire a greater angular speed after a given time.
A car weighs 1800 kg. The distance between its front and back axles is 1.8 m. Its
centre of gravity is 1.05 m behind the front axle. Determine the force exerted by the
level ground on each front wheel and each back wheel.
A non-uniform bar of weight W is suspended at rest by two strings of negligible
weight as shown in Fig.6.33. The angles made by the strings with the vertical are
36.9° and 53.1° respectively. The bar is 2 m long. Calculate the distance d of the
centre of gravity of the bar from its left end.
Two particles, each of mass m and speed v, travel in opposite directions along parallel
lines separated by a distance d. Show that the angular momentum vector of the two
particle system is the same whatever be the point about which the angular momentum
is taken.
Find the components along the x, y, z axes of the angular momentum l of a particle,
whose position vector is r with components x, y, z and momentum is p with
components px
, py
and pz
. Show that if the particle moves only in the x-y plane the
angular momentum has only a z-component.
Show that a.(b × c) is equal in magnitude to the volume of the parallelepiped formed
on the three vectors , a, b and c.
Show that the area of the triangle contained between the vectors a and b is one half
of the magnitude of a × b
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