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To practice Problem-Solving Strategy 7.1 Rotational 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? What is the distance r_n between the point of application of n^vector and the axis of rotation? What is the distance r_w between the point of application of w^vector and the axis? Enter your answers in meters separated by a comma. r_n, r_w = _______ m, m Use the information that you have gathered to find the angular acceleration. Determine whether your answer makes sense.

Answer 1

Solution: Recall that the magnitude τ of a torque is defined by τ TF sin φ, where r is the distance from the pivot point to the point of application for the force, F is the magnitude of the force that exerts the torque, and φ is the angle between the force and the line connecting the pivot to the point of application Find the distance from the axis for each force acting on the pencil What is the distance ro between the point of application of ri and the axis of rotation? What is the distance rw between the point of application of and the axis? What is the distance rE between the point of application of f and the axis? Recall that the axis of rotation in this problem is horizontal. ANSWER: rn, Tw 0,7.50x10, m