Angular acceleration and Torque

In summary, the rod is released at an angle of 30◦ beneath the horizontal and experiences an angular acceleration of rad/s2 immediately after being released.
  • #1
nazerofsun
7
0

Homework Statement



A uniform 6 kg rod with length 18 m has
a frictionless pivot at one end. The rod is
released from rest at an angle of 30◦ beneath
the horizontal.What is the angular acceleration of the rod
immediately after it is released? The moment
of inertia of a rod about the center of mass
is 1/12 mL2 , where m is the mass of the rod and L is the length of the rod. The moment
of inertia of a rod about either end is 1/3 mL2, and the acceleration of gravity is 9.8 m/s2 .
Answer in units of rad/s2.



Homework Equations


I(alpha), Torque


The Attempt at a Solution


I swear I've spent the past 3 hours searching for solutions online, my head, book, and nothing that has given me any answer that is reasonable. So, this is my last resort. :P

From all of the types of ways I've found to solve it, this is the one I truly understand,

since it is a rod with axis at the end it's inertia is 1/3m(length)^2,

1/3m(length)^2*(alpha) = Torque= r*(Force)= (length)/2 *mg*cos(30)

then solve for alpha,

This is where I get confused... r*force is a cross product right? so shouldn't it be (Length)/2 * mg*sin(30)? and i don't even know if my right side of my equation is even right =.=\ does gravity even affect torque? it should... I've seen problems like this with a mass attached at the end to give extra torque and they don't even mention gravity acting upon the rod on the right side. I seriously won't sleep till I answer this!
 
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  • #2
oh also, even made sure I was using the right moment of inertia by proving it with the parallel axis theorem
 
  • #3
Torque = I*alpha
Torque = Force*Distance

You know I, find torque, then solve for alpha.
Draw a free body diagram and use trig to find the torque.

The only force acting on the rod is gravity on its center of mass.

The right side of your equation is correct. Draw a freebody diagram and you will see that
the force of gravity normal to the bar in that position is mg*cos(30).
 
Last edited:
  • #4
I received 4.24352 rad/s^2... for alpha.

well, i already attempted my max amount of tries on it so I missed it :P but, I was able to verify it with another problem I have in my notes.

Thanks again. you helped me notice that the cross product still holds F*r*sin(theta) but the theta is a different one, 90-30, which is totally obvious right? haha, i need to take a break =.=\
Just what I get messed up on is which angle is which theta, the free body diagram helps alot, but even then I question myself :P. I need to remember from perpendicular to the rod to the vector of gravity is the same angle as the tilt from the horizontal. cheers! time to make a big glass of pepsi.
 

What is angular acceleration?

Angular acceleration is a measure of how quickly the rotational velocity of an object changes over time. It is typically measured in radians per second squared.

What factors affect angular acceleration?

The main factors that affect angular acceleration are the magnitude of the applied torque, the moment of inertia of the object, and the angle at which the torque is applied.

What is torque?

Torque is a measure of the force that causes an object to rotate around an axis. It is calculated by multiplying the force applied to the object by the distance from the axis of rotation.

How is angular acceleration related to torque?

Angular acceleration is directly proportional to the applied torque and inversely proportional to the moment of inertia. This means that a larger torque or a smaller moment of inertia will result in a greater angular acceleration.

How is angular acceleration different from linear acceleration?

Angular acceleration refers to changes in the rotational velocity of an object, while linear acceleration refers to changes in the linear velocity (speed and direction) of an object. Additionally, angular acceleration is measured in radians per second squared, while linear acceleration is measured in meters per second squared.

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