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.

Respuesta :

alekos
t1 = ω1/α.............

the time t1 it takes to accelerate:

[tex]\large{\boxed{\bold{t_1=\frac{\omega_1 }{\alpha}}}}[/tex]

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

[tex]\rm \omega=\dfrac{\Delta \theta}{\Delta t}[/tex]

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

[tex]\rm \omega=\omega o+\alpha t[/tex]

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

[tex]\large{\boxed{\bold{t=\frac{ \omega_1}{\alpha }}}[/tex]

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