You push a disk-shaped platform tangentially on its edge 2.0 m 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 its speed at the edge to 7.0 m/s.

Answer: 40.84 m

Explanation:

Given

Radius of the disk, r = 2m

Velocity of the disk, v = 7 rad/s

Acceleration of the disk, α = 0.3 rad/s²

Here, we use the formula for kinematics of rotational motion to solve

2α (θ - θ•) = ω² - ω•²

Where,

ω• = 0

ω = v/r = 7/2

ω = 3.5 rad/s

2 * 0.3 (θ - θ•) = 3.5² - 0

0.6 (θ - θ•) = 12.25

(θ - θ•) = 12.25 / 0.6

(θ - θ•) = 20.42 rad

Since we have both the angle and it's radius, we can calculate the arc length

s = rθ = 2 * 20.42

s = 40.84 m

Thus, the needed distance is 40.84 m