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Question 12.169: The slotted link is pinned at O, and as a result of the cons...

The slotted link is pinned at O, and as a result of the constant angular velocity \dot { \theta } = 3 rad/s it drives the peg P for a short distance along the spiral guide r = (0.4\,\theta) m , where \theta is in radians. Determine the velocity and acceleration of the particle at the instant it leaves the slot in the link, i.e., when r = 0.5 m.

Question Data is a breakdown of the data given in the question above.
  • The slotted link is pinned at point O.
  • The constant angular velocity is \dot θ= 3 rad/s.
  • The spiral guide equation is r = 0.4θ m.
  • The particle leaves the slot when r = 0.5 m.
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Step 1:
The given equations describe the motion of an object in...
Step 2:
To find the values at r = 0.5 m, we substitute this val...
Step 3:
We can then find the values of the radial velocity, ẋ, ...
Step 4:
The tangential velocity, vθ, can be found by multiplyin...
Step 5:
The radial acceleration, ar, can be found by substituti...
Step 6:
The tangential acceleration, aθ, can be found by substi...
In summary, at r = 0.5 m, the object has a radial veloc...

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