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## Homework Statement

R = 49 mA tall, cylindrical chimney falls over when its base is ruptured. Treat the chimney as a thin rod of length 49.0 m. Answer the following for the instant it makes an angle of 29.0° with the vertical as it falls. (Hint: Use energy considerations, not a torque.)

(a) What is the radial acceleration of the top?

(b) What is the tangential acceleration of the top?

(c) At what angle θ is the tangential acceleration equal to g?

theta = 29°

## Homework Equations

Kinematic equations for Rotational Forces and Circular motion

Kinetic Energy = 1/2*I*w^2

## The Attempt at a Solution

First I can find the moment of Inertia for a rod, which is: 1/12 * MR^2

However I need to use the parallel axis theorem to find: 1/12*MR^2 + M(R/2)^2

Simplifying this I get:

**I = 1/3 * M * R^2**

I already know that I can find the angular velocity through conservation of energy:

**KE + U initial = KE + U final**

(these can be found if we follow the kinematics of the center of mass)

**0 + Mg(h/2) = 1/2*I*w^2 + Mg(R/2 * cos(theta))**

g = 1/3 * R * w^2 + g*cos(theta

g*(1-cos(theta)) = 1/3 * R * w^2

w^2 = (3g * (1-cos(theta))) / R

g = 1/3 * R * w^2 + g*cos(theta

g*(1-cos(theta)) = 1/3 * R * w^2

w^2 = (3g * (1-cos(theta))) / R

From circular motion kinematics we know that:

**a(radial) = (v^2) / R**

We also know that:

**v = w*R**

So combining them I get:

**a(radial) = (w*r)^2 / R**

a(radial) = w^2 * R

a(radial) = w^2 * R

After plugging in values I get:

**a(radial) = 3 * g * (1 - cos(theta))**

a(radial) = 3 * 9.81 * (1 - cos(29))

a(radial) = 3.69 m/s^2

a(radial) = 3 * 9.81 * (1 - cos(29))

a(radial) = 3.69 m/s^2

From there I need to find the tangential acceleration, but I can't seem to get a decent answer.

I know that:

**a(tangential) = alpha * R**

and using kinematic equations I can find that

**w^2 = 2(alpha)*(theta)**

alpha = (w^2) / (2*(theta'))

alpha = (w^2) / (2*(theta'))

Where theta' here would be a radian measure or 29*(pi/180)

but this ends up giving me a value of 0.0744, which can't be right. Am I missing something?