140
4 Rotational Dynamics
Fig. 4.2
4.17 An ice skater spins at 4π rad/s with her arms extended.
(a) If her moment of inertia with arms folded is 80% of that with arms
extended, what is her angular velocity when she folds her arms?
(b) Find the fractional change in kinetic energy.
4.18 A sphere of radius R and mass M rolls down a horizontal plane. When it
reaches the bottom of an incline of angle θ it has velocity v 0 . Assuming that
it rolls without slipping, how far up the incline would it travel?
4.19 A body of mass m is attached to a light string wound around a pulley of mass
M and radius R mounted on an axis supported by fixed frictionless bearings
(Fig. 4.3). Find the linear acceleration ‘a’ of m and the tension T in the string.
Fig. 4.3
4.20 A light string is wound several times around a spool of mass M and radius R.
The free end of the string is attached to a fixed point and the spool is held so
that the part of the string not in contact with it is vertical (see Fig. 4.4). If the
spool is let go, find the acceleration and the tension of the string.
4 Rotational Dynamics
Fig. 4.2
4.17 An ice skater spins at 4π rad/s with her arms extended.
(a) If her moment of inertia with arms folded is 80% of that with arms
extended, what is her angular velocity when she folds her arms?
(b) Find the fractional change in kinetic energy.
4.18 A sphere of radius R and mass M rolls down a horizontal plane. When it
reaches the bottom of an incline of angle θ it has velocity v 0 . Assuming that
it rolls without slipping, how far up the incline would it travel?
4.19 A body of mass m is attached to a light string wound around a pulley of mass
M and radius R mounted on an axis supported by fixed frictionless bearings
(Fig. 4.3). Find the linear acceleration ‘a’ of m and the tension T in the string.
Fig. 4.3
4.20 A light string is wound several times around a spool of mass M and radius R.
The free end of the string is attached to a fixed point and the spool is held so
that the part of the string not in contact with it is vertical (see Fig. 4.4). If the
spool is let go, find the acceleration and the tension of the string.