The slotted link is pinned at O, and as a result of the constant angular velocity θ = 3 rad/s it drives the peg P for a short distance along the spiral guide r = (0.4θ) m , where θ is in radians. Determine the radial and transverse components of the velocity and acceleration of P at the instant θ

Question

The slotted link is pinned at O, and as a result of the constant angular velocity [latex]\dot { heta }[/latex] = 3 rad/s it drives the peg P for a short distance along the spiral guide r = (0.4[latex]\, heta[/latex]) m , where [latex] heta[/latex] is in radians. Determine the radial and transverse components of the velocity and acceleration of P at the instant [latex] heta=\pi[/latex] /3 rad.

Accepted Answer

[latex]\begin{array}{rl}\dot{ heta}=3 \,\mathrm{rad} / \mathrm{s} & r=0.4 heta \\dot{r} & =0.4 \dot{ heta} \\ddot{r} & =0.4 \ddot{ heta}\end{array}[/latex]

At [latex] heta=\frac{\pi}{3}, \quad r=0.4189[/latex]

[latex]\begin{gathered}\dot{r}=0.4(3)=1.20 \\ddot{r}=0.4(0)=0 \v=\dot{r}=1.20 \mathrm{~m} / \mathrm{s} \v_ heta=r \dot{ heta}=0.4189(3)=1.26 \mathrm{~m} / \mathrm{s} \a_r=\ddot{r}-r \dot{ heta}^2=0-0.4189(3)^2=-3.77 \mathrm{~m} / \mathrm{s}^2 \a_ heta={r} \ddot{ heta}+2 \dot{r} \dot{ heta}=0+2(1.20)(3)=7.20 \mathrm{~m} / \mathrm{s}^2\end{gathered}[/latex]

Question 12.167: The slotted link is pinned at O, and as a result of the cons...

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