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4 Rotational Dynamics
4.55 A metre stick of length l and mass M is placed on a frictionless horizontal
table. A hockey ball of mass m sliding along the table perpendicular to the
stick with speed v strikes the stick elastically at distance d from the centre of
the metre stick. Find d if the ball is to be brought to rest immediately after the
collision (Fig. 4.13).
Fig. 4.13
4.56 A uniform solid cylinder of mass m and radius R is set in rotation about its
axis and lowered with the lateral surface on to the horizontal plane with initial
centre of mass velocity v 0 . If the coefficient of friction between the cylinder
and the plane is μ, find
(a) how long the cylinder will move with sliding friction.
(b) the total work done by the sliding friction force on the cylinder.
4.57 Two identical cylinders, each of mass m, on which light threads are wound
symmetrically are arranged as in Fig. 4.14. Find the tension of each thread in
the process of motion. Neglect the friction in the axle of the upper cylinder.
Fig. 4.14
4.58 A uniform circular disc of radius r and mass m is spinning with uniform
angular velocity ω in its own plane about its centre. Suddenly a point on its
circumference is fixed. Find the new angular speed ω and the impulse of the
blow at the fixed point.
4 Rotational Dynamics
4.55 A metre stick of length l and mass M is placed on a frictionless horizontal
table. A hockey ball of mass m sliding along the table perpendicular to the
stick with speed v strikes the stick elastically at distance d from the centre of
the metre stick. Find d if the ball is to be brought to rest immediately after the
collision (Fig. 4.13).
Fig. 4.13
4.56 A uniform solid cylinder of mass m and radius R is set in rotation about its
axis and lowered with the lateral surface on to the horizontal plane with initial
centre of mass velocity v 0 . If the coefficient of friction between the cylinder
and the plane is μ, find
(a) how long the cylinder will move with sliding friction.
(b) the total work done by the sliding friction force on the cylinder.
4.57 Two identical cylinders, each of mass m, on which light threads are wound
symmetrically are arranged as in Fig. 4.14. Find the tension of each thread in
the process of motion. Neglect the friction in the axle of the upper cylinder.
Fig. 4.14
4.58 A uniform circular disc of radius r and mass m is spinning with uniform
angular velocity ω in its own plane about its centre. Suddenly a point on its
circumference is fixed. Find the new angular speed ω and the impulse of the
blow at the fixed point.