Determine a formula for the angular velocity πœ” as a function of time.

Chapters 10 and 12 Written Homework
Be sure to show all your work, particularly for oddnumbered
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 = 4.2𝑑2 βˆ’
9.0𝑑, where 𝛼 is in π‘Ÿπ‘Žπ‘‘/𝑠2 and 𝑑 in seconds. If the wheel starts from rest (πœƒ = 0,
πœ” = 0, at 𝑑 = 0):

a) Determine a formula for the angular velocity πœ” as a function of time.

b) Determine a formula for the angular position πœƒ as a function of time.

c) Evaluate πœ” and πœƒ at 𝑑 = 2.0 𝑠.

10 – 51: An Atwood machine consists of two
masses, π‘šπ΄ = 65 π‘˜π‘” and π‘šπ΅ = 75 π‘˜π‘”,
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 π‘š and mass 6.0 π‘˜π‘”.

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 413, assuming I = 0 for the pulley.)

There is one more question on the next page.

12 – 17: A traffic light hangs from a pole as shown below. The uniform aluminum

pole 𝐴𝐡 is 7.20 π‘š long and has a mass of 12.0 π‘˜π‘”. The mass of the traffic light is
21.5 π‘˜π‘”.

d) Determine the tension in the horizontal massless cable 𝐢𝐷.

e) Determine the vertical and horizontal components of the force exerted by
the pivot 𝐴 on the
horizontal components