AP Physics C: Mechanics 5.2: Linear & Rotational Motion

Practise connecting rotational and linear motion by using gear radii to compare angular speeds and applying a = rα to find tangential acceleration.

Exam points

Use equal contact speeds and gear tooth counts to compare angular velocities.
Apply a = rα to convert angular acceleration into tangential acceleration at a point.

[Maximum number: 2]

Figure for Question 5.2.A—Describe the linear motion of a point on a rotating rigid system that corresponds to the rotational motion of… question 1 — AP Physics C: Mechanics

Mech. 3. A uniform, rigid, thin board that is 2.4 m long and weighs 200 N is attached to a post by a pivot at point P and hangs over the edge of a building, as shown above. A crate weighing 400 N is attached to the right end of the board. The left end of the board, 0.80 m from the pivot, is attached to a light vertical wire anchored at the other end to keep the board from rotating.

(d) Suppose that the wire breaks and the board begins to pivot about point P. Calculate each of the following.

ii. The magnitude of the initial linear acceleration of the left end of the board

ii. 2 points For a correct relationship between angular and linear acceleration $a=r \alpha$ $a=(0.80 \mathrm{~m})\left(6.13 \mathrm{rad} / \mathrm{s}^{2}\right)$ For an answer consistent with part (d)i. $a=4.9 \mathrm{~m} / \mathrm{s}^{2} \quad\left(\right.$ or $5.0 \mathrm{~m} / \mathrm{s}^{2}$ using $\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

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5.2.A—Describe the linear motion of a point on a rotating rigid system that corresponds to the rotational motion of… question 1