To practice Problem-Solving Strategy 12.1 for rotational dynamics problems. Supp

Question

To practice Problem-Solving Strategy 12.1 forrotational dynamics problems. 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 cmand an average mass of 10.0 g . Assume the tip of the pencil does not slip as it falls. Identify and draw the forces that act on the pencil. Be certain to draw each force at the correct location (the point at which the force acts on the pencil). The black dot represents the center of mass of the pencil. file:///Users/alnasermm/Desktop/Screen%20Shot%202014-04-06%20at%201.42.25%20PM.png To practice Problem-Solving Strategy 12.1 forrotational dynamics problems. To practice Problem-Solving Strategy 12.1 forrotational dynamics problems. 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 cmand an average mass of 10.0 g . Assume the tip of the pencil does not slip as it falls. Identify and draw the forces that act on the pencil. Be certain to draw each force at the correct location (the point at which the force acts on the pencil). The black dot represents the center of mass of the pencil. file:///Users/alnasermm/Desktop/Screen%20Shot%202014-04-06%20at%201.42.25%20PM.png file:///Users/alnasermm/Desktop/Screen%20Shot%202014-04-06%20at%201.42.25%20PM.png

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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