Dynamics help: variable acceleration and angular velocity

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SUMMARY

The discussion focuses on solving two dynamics problems involving variable acceleration and angular velocity. For the first problem, the motorcycle's speed is calculated to be 1.5 m/s after 5 seconds, using the kinematic equation v = u + at with an initial speed of 1 m/s and an acceleration of 0.1 m/s². The second problem involves determining the velocity and acceleration of a collar moving along a rotating rod, with the collar's speed given by r = 4t² m/s. The need for clarity in separating unrelated problems is also emphasized.

PREREQUISITES
  • Understanding of kinematic equations, specifically v = u + at
  • Knowledge of angular velocity and its implications in dynamics
  • Familiarity with radial and tangential acceleration concepts
  • Basic calculus for relating dx/dt and dy/dt in motion equations
NEXT STEPS
  • Study the principles of angular motion and its equations
  • Learn about radial and tangential acceleration calculations
  • Explore the application of kinematic equations in non-linear motion
  • Investigate the relationship between speed, velocity, and acceleration in dynamics
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Students studying dynamics, mechanical engineers, and anyone interested in understanding variable acceleration and angular velocity in motion problems.

medynamics
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I have to do these 2 problems for homework, but I can't figure them out. Any help would be appreciated.

1. The motorcycle is traveling at 1m/s when it is at A(the origin). If the speed is then increased at \dot{V} = .1 m/s^2, determine its speed and acceleration at the instant t = 5 seconds. The motorcycle is following the curve y = 0.5 x^2.2. Rod OA rotates counterclockwise with a constant angular velocity of θ = 6 rad/s. Through mechanical means collar B moves along the rod with a speed of r = 4 t^2 m/s, where t is in seconds. If r = 0 when t = 0, determine the magnitudes of velocity and acceleration of the collar when t = 0.75 sec.

This is the link to the image for question 2:
http://s1308.beta.photobucket.com/user/jackcastle618/media/Dynamics4_zps5a431c20.jpg.html
 
Last edited:
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For question 1, start with the Kinematic Equations, specifically v = u + at
 
so using v = u + at:

v = 1m/s + .1(5)
v = 1.5 m/s

now I need a. i believe i need to find radial and tangential a?
so i have a = vdot
so a_r = .1 m/s^2
but how do I get the acceleration that is based on the curve y = .5x^2?
 
CaptainEvil said:
For question 1, start with the Kinematic Equations, specifically v = u + at
I don't think you can use that here. The rate of increase of speed is constant, but that's not the same as acceleration as strictly defined. Acceleration is a vector, or a component of a vector in a consistent direction.
medynamics, try to write down some equations relating dx/dt, dy/dt etc.

It's not a good idea to put two unrelated problems in the same thread.
 

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