Faculty of
Engineering
and
ENPH 131
Last Name:
Seminar 11
First Name:
Rotation of Rigid Bodies
Department of
Physics
ID Number:
Starting April 12, 2010
Seminar Section:
Please do all work on handout and box final numerical answers.
1. The angle
(in radian) is given as a function of time by
. At t = 0.5 s, determine the
magnitude of
(a) [1 marks] the velocity of point A and
(b) [2 marks] the tangential and normal components of acceleration of point A.
2. The radius of the pulley is 100 mm and the moment of inertial about its axis is I = 0.7 kg-m2. The two
masses mA = 25 kg and mB = 5 kg. Assume no slipping between the cable and the pulley. If the system is
released from rest, determine
(a) [5 marks] the tensions TA and TB,
(b) [1 marks] the speed of mass A when t = 0.5 s and
(b) [1 marks] the distance mass A travels in 0.5 s.
3. Consider 4 rigid bodies: (1) a thin-walled hollow cylinder (mass mH), (2) a solid sphere (mass mS), (3)
a solid cylinder (mass mC) and (4) a rectangular block (mass mB). These 4 rigid bodies move down
ramps that are all inclined at the same angle with respect to the horizontal. The hoop, disc and sphere
all roll without slipping down their respective planes, while the block slides without friction.
(a) [6 marks] Determine the linear accelerations of the centers of mass of the four rigid bodies. Express
your answers in terms of g and .
(b) [4 marks] Determine the minimum coefficient of static friction required for the cylinders and the
sphere to roll without slipping, given that
.
The moment of inertia ICM with respect to an axis through the center of mass of the following objects of
mass M are as follows:
Thin-walled hollow cylinder with radius R, ICM = MR2;
Solid sphere with radius R,
ICM = (2/5) MR2;
Solid cylinder with radius R,
ICM = (1/2) MR2.