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posted by  M123 on 11/2/2009 10:05:01 AM  |  status: Closed  |  Earned Karma: 25

Help with Newton's 2nd Law for rotational motion, please!!

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N/A N/A N/A N/A 11/2/2009 at 9:00:00 PM
Question Details:
The drawing shows two identical systems of objects; each consists of the same three small balls connected by massless rods. In both systems the axis is perpendicular to the page, but it is located at a different place, as shown. The same force of magnitude F is applied to the same ball in each system (see the drawing). The masses of the balls are m1 = 8.4 kg, m2 = 5.2 kg, and m3 = 5.0 kg. The magnitude of the force is F = 446 N. (a) For each of the two systems, determine the moment of inertia about the given axis of rotation. (b) Calculate the torque (magnitude and direction) acting on each system. (c) Both systems start from rest, and the direction of the force moves with the system and always points along the 4.00-m rod. What is the angular velocity of each system after 5.19 s?
(a) IA  =   
IB  =   
(b) τA =   
τB =   
(c) ωA =   
ωB =   

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posted by john_r on 11/3/2009 3:08:08 PM  |  status: Live
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Response Details:


(a)
   the moment of inertia of each system will be
   for the system A
   I = m1 r12 + m2 r22 + m3 r32 
     = (8.40 kg) (0 m)2 + (5.2 kg) (3.00 m)2 + (5.00 kg) (5.00 m)2
     = ......... kg.m2
   for the system B
   I = m1 r12 + m2 r22 + m3 r32 
     = (8.4 kg) (5.00 m)2 + (5.2 kg) (4.00 m)2 + (5.0 kg) (0 m)2
     = ......... kg.m2
(b)
   if same force of magnitude F = 446 N the torque will not be the saeme
   we know that
   τ = F l
   where l = 3.00 m
   in the system B the lever arm is l = 0, since the line of action of the force passes through the axis
   of rotation 
   for the system A the torque will be
   τ = - F l
      = - (446 N) (3.00 m)
      = ....... N.m
   for the system B the torque will be
   τ = F l
      = (446 N) (0 m)
      = 0 N.m

(c)
   the equation for the angular velocity is givenn by

   ω = ωo + α t
   but α = (Σ τ / I)

   where Σ τ is the net torque and I is the moment of inertia
   in both the systems start from rest the initial angular velocity ωo = 0 rad/s

   final angular velocity are after t = 10 s
   for system A

    ω = ωo + (Σ τ / I) t
        = ........ rad/s

   for system B
    ω = ωo + (Σ τ / I) t
        = ........ rad/s

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