Lucy M.

asked • 04/21/18

Find the angular velocity of the system after 12 seconds

The angular acceleration of a system is described by the following equation: a(t)=d^2Radians/dt^2=10cos (5t). 
Find the angular velocity of the system in radians after 14 seconds

Arturo O.

In order to solve this problem completely, you need to also state 2 initial conditions, such as θ(0) and ω(0).  Without them, there will be 2 undetermined constants in the solution.
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04/21/18

Lucy M.

a(t)=d2θ/dt2=10cos(5t)
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04/22/18

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Arturo O. answered • 04/22/18

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You can integrate α(t) to get ω(t), but there will be an undetermined constant, unless an initial condition is specified, as I stated in my Comment.
 
ω(t) = ∫α(t)dt = ∫10cos(5t)dt = 2sin(5t) + c1
 
More information is needed to find the value of the constant c1, such as ω(0) or at some other time.  After you determine c1, evaluate ω(t) at t = 12 and 14 seconds.
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Arturo O.

By the way, the correct units for angular velocity are radians/second, not just radians.
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04/22/18

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