**First Examination
**

Physics 104

22 February 1977
#1. The ** angular speed ** of the earth about its axis is most nearly equal to

#2. A flywheel completes** 40 revolutions **as it slows from an angular
speed of **1.5 radians/sec** to a complete stop. Assuming uniform
acceleration, the time (**in seconds**) required for it to come to rest
is most nearly equal to

**Answer:**

#3. A force __F__ = 2 __k__ Newtons acts upon a particle of
mass **3.0 kg** which is located at __r__ = (2 __i__ + 2 __j )__
meters. (See sketch.) The torque (**in Newton-meters**)
acting on the particle about an axis through the origin and normal to r is most
nearly equal to

**Answer:**

#4. With center and spokes of negligible mass, a certain bicycle
wheel has a thin rim of radius **R** and a weight of **W**; it can turn on
its axle with negligible friction. A man holds the wheel above his head
with the axis vertical while he stands on a turntable free to rotate without
friction. The wheel rotates clockwise, as seen from above, with an angular
speed **w**_{o}, and the turntable is initially at rest.
The rotational inertia of wheel-plus-man-plus-turntable about he common axis of
rotation is **I**. The man's hand suddenly stops the rotation of the wheel
relative to the turntable. The resulting ** angular velocity** (as seen
from above) is given by

**Answer:**

#5. A carousel of radius **2.4 meters** is initially at rest, but is free to
rotate about its central axis. Its moment of inertia about its axis is **100
kg m**^{2}. A **30 kg** child runs along the ground at a
speed of **6.0 m/sec**, in a direction tangent to the rim of the carousel,
and then jumps on. The consequent angular speed (**in radians/sec**) of
the carousel is most nearly equal to
**Answer:**

#6. Four objects, each of mass **m = 3 kg, **are placed in a rectangular
array as shown. The moment of inertia (**in kg m**^{2}) of this
array about an axis perpendicular to the plane passing through the geometrical
center is most nearly equal to.

**Answer:**

#7. A spool of mass **m** has a cord wrapped about its center,
and a force **F** acts on it as shown in the sketch. If the spool rolls
without slipping on the table top, and it has a rotational inertia **I**_{c}
about the
axis through its center, then its ** angular acceleration** is

**Answer:**

#8. A **four-foot** uniform beam weighing **160 pounds** is hinged at one
end (**point 0**). It is held in a horizontal position by a cable as
shown. The **vertical component** of the force exerted by the hinge on
the boom is most nearly equal to

**Answer:**

#9. A disk of mass ** m** and radius **R** is rolling around a level surface with speed
** v**_{0}. It
encounters an incline of angle **q**. The
distance * l* that the disk will roll up the incline is most nearly equal to
(Assume no slipping)

**Answer:**

#10. A ** 2 kilogram** stick which is ** 3 meter**s long lies in a north-south direction on a sheet of ice.
It is pushed by a ** 30 Newton** force applied at one end and directed East. The initial angular
acceleration (**in rad/sec**^{2}) is most nearly equal to

**Answer:**

#11. A massless rope is wrapped around a disk of radius **R** and
mass **M**. The disk is free to turn about a horizontal axle through
its axis. The free end of the rope is attached to a mass **m**, as
shown. The system is released from rest. The tension in the
rope as the mass **m** falls is most nearly equal to

**Answer**

#12. A **0.10 kg** block slides back and forth along a straight line on a
frictionless horizontal surface. Its displacement from equilibrium (**x =
0**)
is given by
** x = 10 cos (10pt +
p/2)**
with ** x in cm** and ** t in seconds**. The linear frequency of
oscillation (**in cycles/sec**) is most nearly equal to

**Answer:**

#13. The maximum horizontal force (**in Newtons**) acting on the block of
problem **#12** is most nearly equal
to

**Answer:**

#14. The total energy (**in Joules**) of the system in problem** #12** is most nearly
equal to

**Answer:**

#15. A long uniform rod of length **L** and mass ** M ** is free to rotate in a
horizontal plane about a vertical axis through its center. A pair of
springs of equal force constants **k** are connected horizontally between the
end of the rod and a fixed wall, as shown. the differential equation of
motion of the rod when the rod is pushed slightly to one side (rotating it
through a small angle, **q**) and released is
given by

**Answer:**