Question 1 of 4 · Rigid-Body Kinematics · Intermediate · About 22 min

Motor-driven single rotating link

A slender link $OA$ of length $0.65\,\mathrm{m}$ rotates in a vertical plane around fixed pin $O$ . At the instant shown, its orientation is $35^\circ$ above the positive horizontal axis, angular velocity is $4.0 r a$ counterclockwise and angular acceleration is clockwise. Find the Cartesian velocity and acceleration components of endpoint , and identify normal and tangential acceleration directions.

A straight slender link 0.65 m long from fixed pin O at lower left to free end A, 35 degrees above a thin dashed horizontal line through O. Mark the 35 degree angle. Around O, draw two separate curved arrows: a counterclockwise arrow close to the pin and a clockwise arrow further out. Labels: O; A; 35°; 0.65 m beside the link; ω = 4 rad/s on the counterclockwise arrow; α = 2 rad/s² on the clockwise arrow — Schematic, not to scale unless dimensions are given.

Given

$OA=0.65$ m; $\theta=35^\circ$
$\omega=+4$ rad/s

Find

$\mathbf v_A$
$\mathbf a_A$
Normal and tangential directions

Assumptions

All members and connections are idealised as specified in the question.
Use g = 9.81 m/s^2 where gravitational acceleration is required.

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Motor-driven single rotating link

Given

Find

Assumptions

Worked solution