A wheel starts from rest and has an angular acceleration that is given by $\alpha$ (t)= (6.0 rad/s⁴)t^2. After it has turned through 10 rev its angular velocity is: A)63 rad/s B)75 rad/s C)89 rad/s D)130 rad/s E)210 rad/s

Question

Quizplus · Accepted Answer

Given,

Angular acceleration (α) = (6.0 rad/s²)t

Number of revolutions (n) = 10

Let's calculate the final angular velocity (ωf) of the wheel using the following formula:

ωf² = ωi² + 2αnπ

Here,

Initial angular velocity (ωi) = 0 (as the wheel starts from rest)

Number of revolutions in terms of radians = nπ = 10π radians

Substituting the given values in the formula, we get:

ωf² = 0 + 2(6.0 rad/s²)(10π radians)

ωf = √(120π²) rad/s

ωf ≈ 75 rad/s

Therefore, the best choice is B) 75 rad/s.

A Wheel Starts from Rest and Has an Angular Acceleration α\alphaα

A Wheel Starts from Rest and Has an Angular Acceleration $\alpha$