Question 15.4: Solve Sample Prob. 15.2, using the method of the instantaneo......

Vector Mechanics for Engineers Statics and Dynamics [1686025]

Solve Sample Prob. 15.2, using the method of the instantaneous center of rotation.

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a. Angular Velocity of the Gear. Since the gear rolls on the stationary lower rack, the point of contact C of the gear with the rack has no velocity; point C is therefore the instantaneous center of rotation. We write

v_A=r_A \text v \quad\quad\quad 1.2~ m / s =(0.150~ m ) \text v

V = 8 rad/s i

b. Velocities. As far as velocities are concerned, all points of the gear seem to rotate about the instantaneous center.

Velocity of Upper Rack. Recalling that $v_R=v_B,$ we write

v_R=v_B=r_B \text v \quad\quad\quad v_R=(0.250~ m )(8~ rad / s )=2~ m / s \\ \\ \text v _R=2~ m / s~\text y

Velocity of Point D. Since $r_D=(0.150~ m ) 1 \overline{2}=0.2121~ m$ , we write

\begin{aligned}v_D=r_D \text v \quad\quad v_D=(0.2121~ m )(8 ~rad / s ) & =1.697~ m / s \\\text v _D & =1.697~ m / s \text { a } 45^{\circ}\end{aligned}

15.4.1

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