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Unformatted text preview: Engineering Mechanics - Dynamics ar = r'' − rθ' Chapter 12 2 ar = −158.3 m
aθ = rθ'' + 2r' θ' m aθ = −18.624 2 s Problem 12-142
A particle is moving along a circular path having a radius r. Its position as a function of time is
given by θ = bt2. Determine the magnitude of the particle ’s acceleration when θ = θ1. The
particle starts from rest when θ = 0°.
r = 400 mm Given: b=2 rad θ 1 = 30 deg 2 s θ1 t= Solution: θ = bt t = 0.512 s b 2 θ' = 2b t θ'' = 2b (−r θ' 2)2 + (rθ'' )2 a= a = 2.317 m
2 s Problem 12-143
A particle moves in the x - y plane such that its position is defined by r = ati + bt2j. Determine
the radial and tangential components of the particle’s velocity and acceleration when t = t1.
a=2 Given: ft b=4 s ft t1 = 2 s 2 s t = t1 Solution:
x = at vx = a ft ax = 0 2 s
y = bt 2 vy = 2b t ay = 2b Polar
θ = atan ⎛ ⎟
⎜ ⎝x⎠ θ = 75.964 deg
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This note was uploaded on 08/16/2011 for the course EGN 3321 taught by Professor Christianfeldt during the Spring '08 term at University of Central Florida.
- Spring '08