First Examination
Physics 104
22 February 1977

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

a) 0.26 rad/hr     b) 1000 mi/hr    c) 20o/hr     d) 0.25 rev/hr     e) Zero    

#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:

a) 40       b) 335       c) 27     d) 168     e) 84

#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:
a) 0      b) 4 i  - 4 j      c) 4 k       d) 6      e) -12 i + 12 j     

#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 wo, 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:

a) wo , counterclockwise      b)  Iwo2 , clockwise       c) gIR2wo/W , counterclockwise      
d)  wo,Ig/(WR2) ,  counterclockwise       e) WR2 wo/gI , clockwise 

#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 m2.  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:

a) zero      b) 2.5     c)  1.58     d)  4.32     e)  6.0

#6. Four objects, each of mass m = 3 kg, are placed in a rectangular array as shown.  The moment of inertia (in kg m2) of this array about an axis perpendicular to the plane passing through the geometrical center is most nearly equal to.

Answer:
a) 15      b) 3      c) 6Ö5    d) 12  e) zero

#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 Ic about the axis through its center, then its angular acceleration is

Answer:
a) Fr/Ic      b) Fr/(MR2)       c) Fr Ic /(R-r)MR2         d)   F(R-r)/Ic      e) F(R-r) / (Ic+MR2)

#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:
a) 80 pounds, pointing upward       b) 80 pounds, pointing upward
c) zero       d) 133 pounds, pointing upward e)160 pounds, pointing downward

#9. A disk of mass m and radius R is rolling around a level surface with speed v0. 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:
a) vsin q
b) v02 /(2g)
c)  v02 /(mg sin q)
d)  3v02 /(4g sin q)
e) v02 /(2g sin q)

#10. A 2 kilogram stick which is 3 meters 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/sec2) is most nearly equal to
Answer:
a) 15    b) 30    c)  90     d) 45     e) 10

#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
a) mg     b) mg(1+2m/M)      c) mg/(1+2m/M)     d) m/(m+M)    e) Mg - mg

#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:
a) p/ 2      b) 5    c) 10p      d) 10      e) 20

#13. The maximum horizontal force (in Newtons) acting on the block of problem #12 is most nearly equal to
Answer:
a) 10p     b)  0.10 p2    c) p    d) p2 / 2     e) p2

#14. The total energy (in Joules) of the system in problem #12 is most nearly equal to
Answer:
a) 100p   b)  0.20 p2      c)   p   d) p2 /2   e)  0.05 p2 

#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:
a) d2q/dt2 + kLq/M  =  0
b) d2q/dt2 + kL2q/(4M)  =  0
c) d2q/dt2 + 12kq/(M L2)  =  0
d) d2q/dt2 + 6kq/M  =  0
e) d2q/dt2 + MkL2q/4  =  0