A particle is moving along a circular path having a radius of 4 in. such that it

Question

A particle is moving along a circular path having a radius of 4 in. such that its position as a function of time is given by =cos2t, where is in radians and t is in seconds.

Part A

Determine the magnitude of the acceleration of the particle when = 25 .

Express your answer to three significant figures and include the appropriate units.

A particle is moving along a circular path having a radius of 4 in. such that its position as a function of time is given by =cos2t, where is in radians and t is in seconds.

Part A

Determine the magnitude of the acceleration of the particle when = 25 .

Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

= cos(2t),
= d/dt = -2sin(2t) = -2[1 -cos2(2t)] = -2(1 - 2), when = 250=0.436 rad, = -1.80 rad/s
= d/dt = -4cos(2t) = -4 = -4*0.436 = -1.744rad/s2
tangential acceleration at = R = -6.976in/s2
normal acceleration an = 2R = 12.96in/s2
a = (at2 +an2) = 14.71 in/s2

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