Question

Find the time t1 it takes to accelerate the flywheel to ω1 if the angular acceleration is α. express your answer in terms of ω1 and α.

Answer 1

the time t1 it takes to accelerate:

$\large{\boxed{\bold{t_1=\frac{\omega_1 }{\alpha}}}}$

Further explanation

The speed of the rotating object is called angular velocity. This value is part of circular motion.

The angular velocity is denoted by w including the vector quantity. The unit used is usually rpm (rotation per minute) or radians / sec

Average angular velocity is the ratio of angular displacement to the time interval

$\rm \omega=\dfrac{\Delta \theta}{\Delta t}$

Circular motion with constant acceleration (angular acceleration denoted by α) can be formulated:

$\rm \omega=\omega o+\alpha t$

ωo = initial angular velocity

ω = angular velocity after t

 the flywheel accelerate to ω1, so:

wo = 0 because The flywheel is assumed to be at rest at time t = 0

so the equation becomes:

ω1 = ωo + αt

ω1 = 0 + αt

ω1 = αt

$\large{\boxed{\bold{t=\frac{ \omega_1}{\alpha }}}$

Learn more

the average velocity

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resultant velocity

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velocity position

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Answer 2

T1 = ω1/α.............