To practice Problem-Solving Strategy 12.1 for rotational dynamics problems. Suppose that you are holding a pencil balanced on it
s 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 10.0 g . Assume the tip of the pencil does not slip as it falls.
For this exercise we will use Newton's second law for rotational movement
τ = I α
Where τ is the torque, I the moment of inertia and α the angular acceleration
Torque is the vector product of the distance perpendicular to the axis of rotation and the force that is the weight of the pencil (W); the distance (horizontal) is found with trigonometry
sin 10 = x / (L / 2)
x = L / 2 sin 10
τ = W L / 2 sin 10
τ = m g L / 2 sin 10
The moment of inertia of a pencil can be approximated to a thin rod with an axis of rotation at one end
