Calculating Angular Acceleration of a Rotating Rod

[roam]

Homework Statement

A uniform metre-rule is pivoted to rotate about a horizontal axisthrough the 40-cm mark. The stick has a mass/unit length of $$\mu$$ kg/m and its rotational inertia about this pivot is $$0.093 \mu$$ kg/m². It is released from rest in a horizontal position. What is the magnitude of the angular acceleration of the rod?

Homework Equations

An expression for the magnitude of the torque due to gravitational force about an axis through the pivot: $$\tau =Mg \left( \frac{L}{2} \right)$$

Angular acceleration and torque: $$\sum \tau = I \alpha$$

The Attempt at a Solution

Since $$\mu = \frac{M}{L}$$, and L=0.4m I get

$$\tau = 0.4 \mu g \frac{0.4}{2} = 0.78 \mu$$

$$\alpha = \frac{\tau}{I} = \frac{0.78 \mu}{0.093 \mu} = 8.43$$

But my answer is wrong. The correct answer must be 10.5 rad/s². Could anyone please help me? :(

 

[Doc Al]

An expression for the magnitude of the torque due to gravitational force about an axis through the pivot: $$\tau =Mg \left( \frac{L}{2} \right)$$

Why L/2?

Since $$\mu = \frac{M}{L}$$, and L=0.4m I get

L = 1 m. (It's a meterstick.)

What force provides the torque? How far does that force act from the pivot?

 

[roam]

Why L/2?

Because the gravitational force on the stick acts at its center of mass.

Since the it is pivoted at the 40 cm mark, should I use 60/2 (since the mass is uniformly distributed)?

But this didn't work because I ended up with $$\alpha = 31.6$$...

 

[inky]

Typing error

torque=I*alpha
torque=Fr

 

[Doc Al]

Because the gravitational force on the stick acts at its center of mass.

True, but to calculate the torque due to the weight you need its distance from the pivot. What is that distance?

 

[inky]

True, but to calculate the torque due to the weight you need its distance from the pivot. What is that distance?

distance=0.1 cm

 

[Doc Al]

distance=0.1 cm

The question was meant for the OP, of course.
(And your units are off.)

 

[inky]

The question was meant for the OP, of course.
(And your units are off.)

I am sorry for my wrong units. Actually I should write r=0.1 m. Thanks so much.