- #1
blackheart
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1. A rigid, massless rod has three particles with equal masses attached to it as shown below. The rod is free to rotate in a vertical plane about a frictionless axle perpendicular to the rod through the point P and is released from rest in the horizontal position at t = 0. Assume that m and d are known. (Use the following as necessary: m, d, and g.)
<..2d/3...>
O---------------O-------P----------O
<...d...><...d...>
(a) Find the moment of inertia of the system of three particles about the pivot.
(b) Find the torque acting on the system at t = 0.
(c) Find the angular acceleration of the system at t = 0.
(d) Find the linear acceleration of the particle labeled 3 at t = 0.
(e) Find the maximum kinetic energy of the system.
(f) Find the maximum angular speed attained by the rod. ωf =
(g) Find the maximum angular momentum of the system. Lf =
(h) Find the maximum speed attained by the particle labeled 2. vf =
2.
I was able to solve for (a), (b), (c), and (e). I need help with finding (d), (f), (g), and (h).
3. For (d) finding the linear acceleration, I started with
(torque of mass 3) = (I of mass 3)(alpha)
alpha = 2g/7d
a=r(alpha)
a= 4g/3 but this is incorrect
For part (f), I tried to use conservation of momentum. Li=Lf
(Ii)(wi) = (If)(wf)
It starts from rest so w initial is 0, so I could not solve using this way...
part (g) I think I can solve this if I can solve (f)
How do I approach (h)?
<..2d/3...>
O---------------O-------P----------O
<...d...><...d...>
(a) Find the moment of inertia of the system of three particles about the pivot.
(b) Find the torque acting on the system at t = 0.
(c) Find the angular acceleration of the system at t = 0.
(d) Find the linear acceleration of the particle labeled 3 at t = 0.
(e) Find the maximum kinetic energy of the system.
(f) Find the maximum angular speed attained by the rod. ωf =
(g) Find the maximum angular momentum of the system. Lf =
(h) Find the maximum speed attained by the particle labeled 2. vf =
2.
I was able to solve for (a), (b), (c), and (e). I need help with finding (d), (f), (g), and (h).
3. For (d) finding the linear acceleration, I started with
(torque of mass 3) = (I of mass 3)(alpha)
alpha = 2g/7d
a=r(alpha)
a= 4g/3 but this is incorrect
For part (f), I tried to use conservation of momentum. Li=Lf
(Ii)(wi) = (If)(wf)
It starts from rest so w initial is 0, so I could not solve using this way...
part (g) I think I can solve this if I can solve (f)
How do I approach (h)?