. The radial position r of a particles path is defined by an equation, r = 5 cos (26) m. At the initial time, the angular position is 0 = 0° if the angular velocity of the particle is w= 3t² rad/sec, where It is in seconds, calculate the value of the e-component of acceleration at the instant @ = 30° in m/sec².
. The radial position r of a particles path is defined by an equation, r = 5 cos (26) m. At the initial time, the angular position is 0 = 0° if the angular velocity of the particle is w= 3t² rad/sec, where It is in seconds, calculate the value of the e-component of acceleration at the instant @ = 30° in m/sec².
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Transcribed Image Text:The radial position \( r \) of a particle's path is defined by an equation, \( r = 5 \cdot \cos(2\theta) \) m. At the initial time, the angular position is \( \theta = 0^\circ \). If the angular velocity of the particle is \( \omega = 3t^2 \) rad/sec, where \( t \) is in seconds, calculate the value of the \( \theta \)-component of acceleration at the instant \( \theta = 30^\circ \) in m/sec\(^2\).
Expert Solution
Step 1
The component of the acceleration is given by the formula,
(1)
where is the component of the acceleration, is the radial distance from the origin, and is the angular velocity. And the derivative is taken with respect to time .
Angular velocity is given by the formula,
(2)
where is the angular displacement.
Note: All units are taken in S.I. units for calculations.
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