Angular Displacement and Motion
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1. The angular displacement of a human centrifuge, of length 30 ft, is given by (theta)= 4[t + 30*e^(-.03t)-30]radians where t is in seconds and and t=0 is start up.
If the passenger loses consciousness at an acceleration of 10g's determine the time this would occur.
Verify the tangential acceleration is small compared to the radial acceleration.
2. A rocket is fired vertically and achieves a velocity of 27000 km/hr at an altitude of 350km where it's fuel is exhausted.
How high does the rocket reach before starting it's decent?
3. Just after being struck by a club a golf ball has a velocity of 125ft/sec at an angle of 35 degrees above the horizontal.
Where is the point of impact?
What is the height when x=30 yards?
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1. Since (theta)= 4[t + 30*e^(-.03t)-30], w(angular velocity) = d (theta)/dt = 4[1 - 0.9*e^(-.03t)], and
alpha(angular acceleration)= dw/dt 0.108*e^(-.03t)
the tangential acceleration equals to r*alpha = 3.24*e^(-.03t) (ft/s/s)
the radial acceleration equals to r*w*w = 480*[1 - 0.9*e^(-.03t)] (ft/s/s)
Therefore, when t increases, the radial acceleration increases but tangential acceleration decreases. Assume, after time t the radial acceleration dominates. ...
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