Plane kinetics of rigid bodies

[IsaacCB]

Homework Statement

The uniform 3.6m pole is hinged to the truck bed and is released from the vertical position as the truck starts from rest with an acceleration of 0.9m/s^2. If the acceleration remains constant during the motion of the pole as it reaches the horizontal position what is the angular velocity of the pole as it reaches the horizontal position.

Homework Equations

a(tangential)=mrθ''
a(normal) = mrω^2
ƩMo=Iθ''+Ʃma(vector)d
I=k^2m

The Attempt at a Solution

Using the given formula ƩMo=Iθ''+Ʃma(vector)d to find θ''.

so 0= Iθ''+mrθ''+mg1.8sin(θ)-ma*1.8cos(θ)

haven't been able to get past this point

 

[mark726]

as I am not sure what values to use for the moment of inertia (I) and the distance (d).

Hello,

Thank you for your question. It seems that you are on the right track with using the formula ƩMo=Iθ''+Ʃma(vector)d to find the angular acceleration (θ''). In order to continue, we will need to determine the moment of inertia (I) and the distance (d).

The moment of inertia for a uniform rod rotating about one end is given by I=1/3*ml^2, where m is the mass of the rod and l is the length of the rod. In this case, the mass of the rod is not given, so we will use a variable m to represent it. The length of the rod is given as 3.6m. Therefore, the moment of inertia for the rod is I=1/3*m*(3.6)^2=4.8m.

Next, we need to determine the distance (d) from the pivot point (hinge) to the center of mass of the rod. This distance can be found by using the formula d=l/2, where l is the length of the rod. In this case, the distance from the pivot point to the center of mass is d=3.6/2=1.8m.

Now, we can substitute these values into the formula ƩMo=Iθ''+Ʃma(vector)d to find θ''.

So, 0=4.8m*θ''+m*1.8m*0.9m/s^2+mg*1.8m*sin(θ)-m*0.9m/s^2*1.8m*cos(θ)

Simplifying, we get: 0=4.8m*θ''+1.62m^2+1.8mg*sin(θ)-1.62mg*cos(θ)

From here, we can solve for θ'' by rearranging the terms and solving for it. Once we have the value for θ'', we can use the formula ω=θ' to find the angular velocity (ω) of the pole as it reaches the horizontal position.

I hope this helps. Let me know if you have any further questions. Good luck with your problem!