Rotational Momentum and linear acceleration

[blackheart]

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.)Sorry this is my diagram (I couldn't paste it for some reason)...

distance from P to m3 is (2d/3)
m1-------------m2-------P---------m3 THIS IS THE ROD WITH MASSES
distance between the masses is d
m1, m2, m3 are the same mass(d) Find the linear acceleration of the particle labeled 3 at t = 0.
(torque of mass 3) = (I of mass 3)(alpha)

alpha = 2g/7d

a=r(alpha)

a= 4g/3 but this is incorrect

(f) Find the maximum angular speed attained by the rod. ωf =

(Ii)(wi) = (If)(wf)
It starts from rest so w initial is 0, so I could not solve using this way...

(h) Find the maximum speed attained by the particle labeled 2. vf =

Relevant equations:
L(initial) = L final
L=Iw=mvrsin(theta)
torque = r x F

 

[alphysicist]

Hi blackheart,

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.)


Sorry this is my diagram (I couldn't paste it for some reason)...

distance from P to m3 is (2d/3)
m1-------------m2-------P---------m3 THIS IS THE ROD WITH MASSES
distance between the masses is d
m1, m2, m3 are the same mass


(d) Find the linear acceleration of the particle labeled 3 at t = 0.
(torque of mass 3) = (I of mass 3)(alpha)

alpha = 2g/7d

a=r(alpha)

a= 4g/3 but this is incorrect

Just from looking at these last three equations, it looks like you are setting r=(14/3) d (which is about r=4.67 d). But what should r be for mass 3?

How are you getting that value for the angular acceleration?

(f) Find the maximum angular speed attained by the rod. ωf =

(Ii)(wi) = (If)(wf)

This equation is stating the the angular momentum is conserved. But that is not automatically true for a system; you have to check that it is true. What is the test for whether angular momentum is conserved or not?

Are there any other quantities that are conserved here?

It starts from rest so w initial is 0, so I could not solve using this way...

(h) Find the maximum speed attained by the particle labeled 2. vf =

Relevant equations:
L(initial) = L final
L=Iw=mvrsin(theta)
torque = r x F