August 29, 2007
TA: Tomoyuki Nakayama Tuesday, March 2nd, 2010
PHY 2048: Physic 1, Discussion Section 6839
Quiz 6 (Homework Set # 8)
Name: UFID:
Formula sheets are not allowed. Calculators are allowed. Do not store equations in your calculator. You need to show all of your work for full credit.
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The figure below right shows a uniform disk that can rotate around its center like a merry-go round. The disk has a radius of 5.00 cm and a mass of 80.0 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 = 2.00 s the disk has an angular velocity of 200 rad/s counterclockwise. Force F2 has a magnitude of 0.300 N.
a) What is the angular acceleration of the disk during the time interval between t = 0 and t = 2 s?
Angular acceleration is given by the change in angular velocity divided by time interval. We take positive direction counterclockwise. The angular acceleration is
α = Δω/Δt = (200 - 0)/(2 - 0) = 100 rad/s2
b) What is the angular displacement during the time interval?
We use the kinematic equation for angular displacement. We get
Δθ = (1/2)αΔt2 = 200 rad
c) What is the magnitude of F1?
We apply Newton’s 2nd law in angular form to the disk and solve it for the unknown force F1.
Iα = F2R – F1R ⇒ F1 = F2 – Iα/R = 0.100 N,
where I = (1/2)MR2 = 1.00 × 10-4 kg m2
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