Suppose that you are holding a pencil balanced on its point. If you release the

Question

Suppose that you are holding a pencil balanced on its point. If you release the pencil and it begins to fall, what will be the angular acceleration when it has an angle of 10.0 degrees from the vertical? A typical pencil has an average length of 15.0 cm and an average mass of 10.0g. Calculate the time for the pencil to hit the ground, assuming that it falls from standing perfectly vertical and maintains this angular acceleration.

I tried t=0.61s and it was not the correct answer...can someone help me?

Explanation / Answer

T = I * ?

Moment of Inertia of Long Thin Rod at end is I = m*(L^2) / 3

|r| |F| sin(?) = [m * (L^2) / 3] * ?

|L / 2| |m * g| sin(?) / [m * (L^2) / 3] = ?

3 g sin(?) / (2 * L) = ?

So....

3 (9.8) sin(10) / (2 * 0.15) = 17 rad/s^2 = ? *if accelerating counter clockwise*

If it is accelerating clockwise then ? = -17 rad/s^2

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