Determine a formula for the angular velocity 𝜔 as a function of time.

Chapters 10 and 12 Written Homework
Be sure to show all your work, particularly for odd–numbered
questions. If you end up looking at a solution please cite the
source of your information.
10 – 26: The angular acceleration of a wheel, as a function of time, is 𝛼 = 4.2𝑡2 −
9.0𝑡, where 𝛼 is in 𝑟𝑎𝑑/𝑠2 and 𝑡 in seconds. If the wheel starts from rest (𝜃 = 0,
𝜔 = 0, at 𝑡 = 0):
a) Determine a formula for the angular velocity 𝜔 as a function of time.
b) Determine a formula for the angular position 𝜃 as a function of time.
c) Evaluate 𝜔 and 𝜃 at 𝑡 = 2.0 𝑠.
10 – 51: An Atwood machine consists of two
masses, 𝑚𝐴 = 65 𝑘𝑔 and 𝑚𝐵 = 75 𝑘𝑔,
connected by a massless inelastic cord that
passes over a pulley free to rotate (as shown
below). The pulley is a solid cylinder of radius
𝑅 = 0.45 𝑚 and mass 6.0 𝑘𝑔.
a) Determine the acceleration of each
mass.
b) What percent error would be made if
the moment of inertia of the pulley is
ignored?
Hint: The tensions 𝑭𝑻𝑨 and 𝑭𝑻𝑩 are not
equal. (The Atwood machine was discussed in
example 4–13, assuming I = 0 for the pulley.)
There is one more question on the next page.

pole 𝐴𝐵 is 7.20 𝑚 long and has a mass of 12.0 𝑘𝑔. The mass of the traffic light is
21.5 𝑘𝑔.
d) Determine the tension in the horizontal massless cable 𝐶𝐷.
e) Determine the vertical and horizontal components of the force exerted by
the pivot 𝐴 on the horizontal components