Physics - Rotational Motion?

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? What is the distance r_n between the point of application of n (normal force) and the axis of rotation? What is the distance r_w between the point of application of w (weight; force of gravity) and the axis?

The question is looking for the r_n and r_w in meters. I am not really sure how to go about doing this problem...

Equation help that is given by the problem:
net torque=(moment of Inertia)(angular acceleration)
Moment of Inertia=Summation(m_initial)(r_initial)^2

Thanks!

Answer 1

Assume that the pencil rotates about the point of contact with the floor

without sliding … only two forces act on the pencil … the normal force N

acting vertically upward at the point of contact with the floor and the

weight ( mg ) acting vertically downward at the center of mass of the

pencil … in the absence of friction, no force acts along the horizontal …

according to Newton’s second law for rotational motion …

… torque τ = I α = ( mg ) ( ½ ℓ sin θ ) … where … ℓ = length of the pencil

assumed to be uniform … θ = angle between the vertical line and the pencil

… there is no torque due to the normal force since N passes through the axis

of rotation … with the pencil considered as a thin rod pivoted about one of

its ends, we have … I = ⅓ m ℓ ² … so that … τ = I α = [ ⅓ m ℓ ² ] α … using the

earlier expression for the torque … τ = ( mg ) ( ½ ℓ sin θ ) = [ ⅓ m ℓ ² ] α …

solving for the angular acceleration … α = ( ³ / ₂ ) ( g / ℓ ) sin θ … so that

when θ = 10° … we get … α = ( ³ / ₂ ) ( g / ℓ ) sin 10° …

Answer 2

rn= 0

rw= 7.50*10^-2 (.0750)

Answer 3

around action deals with basically the action which could be in around yet in rotational motions it is going to no longer be in around in spite of the undeniable fact that it is going to be in rotational with admire to any of its suitable factor.