Question

Constants A heavy flywheel is accelerated (rotationally) by a motor that provides constant torque and therefore a constant angular acceleration α. The flywheel is assumed to be at rest at time t=0 in Parts A and B of this problem.

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

t_{1 = ?}

Find the angle θ1 through which the flywheel will have turned during the time it takes for it to accelerate from rest up to angular velocity ω1.

Express your answer in terms of some or all of the following: ω1, α, and t1.

θ1 = ?

Answer 1

w_o = initial angular velocity at t = 0 , = 0 rad/s

w_f = final angular velocity = w₁

t = time taken = t₁

$\alpha$ = angular acceleration

Using the equation

w_f = w_o + $\alpha$t

w₁ = 0 + $\alpha$ t₁

t₁ = w₁ /$\alpha$

$\theta$₁ = angular displacement

Using the equation

$\theta$₁ = w_o t + (0.5) $\alpha$t²

$\theta$₁ = (0) t₁ + (0.5) $\alpha$t₁²

$\theta$₁ = (0.5) $\alpha$t₁²