|
17. Problem 12.11P (HRW) A body of radius R and mass m is rolling smoothly with speed v on a horizontal surface. It then rolls up a hill to a maximum height h. (a) If
(b) What might the body be? |
, what
is the body’s rotational inertia about the rotational axis through its centre of
mass?|
Solution: Click For PDF Version As the body of radius R is rolling smoothly, its
angular speed
K.E.= When the body rolls up a hill to the maximum height
P.E.= The principle of conservation of energy gives us the equation
Solving this equation, we get
Therefore, the body is either a solid cylinder or a disk. |
and speed
of its centre of mass are related by the formula
.
Let the rotational inertia of the body about its axis of rotation passing
through the centre of mass be
. The
kinetic energy of the body will be the sum of the kinetic energy of translation
of its centre of mass,
, and the
kinetic energy of rotation about the axis passing through its centre of mass
. That is
.
.
.