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You push a disk-shaped platform on it’s edge 2.0m from the axle. The platform starts at rest and has a rotational acceleration of 0.30 rad/s2. Determine the distance you must run while pushing the platform to increase it's speed at the edge to 7.0 m/s.

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R = 2 m

α = 0.30 rad/s2

\(\vartheta\) = 7m/s

We use the formula for kinematics of rotational motion to solve

\(\omega^2-\omega_0\,^2\) = 2α(θ - θ0)

∵ \(\omega_0 - 0 \)

\(\omega^2 = 2 \times0.30(\theta -\theta_0)\)

∵ \(\vartheta = r\omega\)

\(\omega = \frac{\vartheta}{r}\)

⇒ \(\frac72 = 3.5 \) rad/s

(3.5)2 = 2 x 0.30 (θ - θ0)

(θ - θ0) = \(\frac{12.25}{0.6}\)

(θ - θ0) = 20.41 rad

Then

S = rθ

S = 2 x 20.41

S = 40.83 m

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