Exam #3
PHYS 201-1M
25 October 2006
Name_________________________
Answer each of the following questions. Circle your final answer. Full credit will be
given only for the correct answer. For errors in the calculations but where the method is
correct, only one point will be deducted. If the chosen method is incorrect, no credit will
be given for that section of the problem. However, if subsequent questions depend on the
missed answer, no points will be deducted if the method and calculations for those
sections are correct, even though the final answer may be wrong.
1) (15 pts) The angular position of a point on a rotating wheel is given by
θ = 1.0t + 4.0t 2 − 8.0t 4 , where θ is in radians and t is in seconds.
a. At t=0, what is the point’s angular position (in radians)?
b. At t=0, what is the point’s angular velocity (in radians/sec)?
c. At t=4 s, what is the point’s angular velocity?
d. At t=2 s, what is the point’s angular acceleration?
2) (20 pts) This figure shows a uniform disk that can rotate around its center like a
merry-go-round. The disk has a radius of 3.00 cm and a mass of 50.0 grams and
is initially at rest. Starting at time t=0, two forces are to be applied tangentially to
the rim as indicated, so that at time t=2.50 s, the disk has an angular velocity of
r
300 rad/s clockwise. Force F1 has a magnitude of 0.200 N. What is the
r
1
magnitude of F2 ? (The moment of inertia for a disk is I = MR 2 .)
2
r
3) (20 pts) A 2.0 kg particle with velocity v = (3.0m / s )iˆ − (5.0m / s ) ˆj is at x=1.0 m
r
and y=3.0 m. It is pulled by a force F = (1.0 N )iˆ − (4.0 N ) ˆj . About the origin,
what are
a. The particle’s angular momentum
b. The torque acting on the particle
c. The rate at which the angular momentum is changing
4) (20 pts) At the instant shown in this figure, a 1.0 kg particle P has a position
r
r
vector r of magnitude 1.5 m and angle θ1 = 25o and a velocity vector v of
r
magnitude 3.0 m/s and angle θ 2 = 30o . Force F , of magnitude 1.0 N and angle
θ3 = 40o , acts on P. All three vectors lie in the xy plane. About the origin, what
are
a. Magnitude of the angular momentum of P
b. Direction of the angular momentum of P
c. Magnitude of the torque acting on P
d. Direction of the torque acting on P
5) (15 pts) An anchor of density 6000 kg/m3 appears 100 N lighter in water than in
air.
a. What is the volume of the anchor?
b. How much does the anchor weigh in air?
6) (10 pts) This figure shows the merging of two streams to form a river. One
stream has a width of 10.2 m, depth of 4.0 m, and current speed of 3.4 m/s. The
other stream is 7.0 m wide, 3.0 m deep, and flows at 2.9 m/s. If the river has
width 10.5 m and speed 2.7 m/s, what is its depth?