A 60 cm diameter wheel accelerates from rest at a rate of 7 rad/s2. After the wheel has undergone 14 rotations, what is the radial component of the acceleration (in m/s2) on the edge the wheel?

The radial component of the acceleration (in m/s2) on the edge the wheel is 369.45 m/s²

Using ω² = ω₀² + 2αθ, we find the final angular speed after 14 revolutions, ω where

So, substituting the values of the variables into the equation, we have

ω² = ω₀² + 2αθ,

ω² = (0 rad/s)² + 2 × 7 rad/s² × 87.965 rad.

ω² = 0 rad²/s² + 1231.504 rad²/s²

ω² = 1231.504 rad²/s²

ω = √(1231.504 rad²/s²)

ω = 35.09 rad/s

We know that the radial acceleration a = rω² where

So, substituting the values of the variables into the equation, we have

a = rω²

a = 0.30 m × (35.09 rad/s)²

a = 0.30 m × 1231.504 rad²/s²

a = 369.45 m/s²

So, the radial component of the acceleration (in m/s2) on the edge the wheel is 369.45 m/s².

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Explanation:

Given that,

Initial angular velocity,

Acceleration of the wheel,

Rotation,

Let t is the time. Using second equation of kinematics can be calculated using time.

Let is the final angular velocity and a is the radial component of acceleration.

Radial component of acceleration,

So, the required acceleration on the edge of the wheel is .