A solid cylinder has a moment of inertia of 2 kg · m². It is at rest at time zero when a net torque given by
$\tau$ = 6t² + 6 (SI units)
Is applied. After 2 s, the angular velocity of the cylinder will be

Question

A solid cylinder has a moment of inertia of 2 kg · m². It is at rest at time zero when a net torque given by

\tau

= 6t² + 6 (SI units)
Is applied. After 2 s, the angular velocity of the cylinder will be

Quizplus · Accepted Answer

We can use the equation

Δθ = (1/2)αt^2

to find the angle rotated by the cylinder in 2 seconds, where α is the angular acceleration given by

α = τ/I

Substituting the given values, we get

α = (6t)/(2 kg·m^2) = 3t kg·m^-2

So,

Δθ = (1/2)αt^2 = (1/2)(3t)(2 s)^2 = 6t

Finally, we can use the equation

ω = Δθ/Δt

to find the angular velocity of the cylinder after 2 seconds, where Δt is the time interval. Substituting the value of Δθ, we get

ω = 6t/2 s = 3t rad/s

So, after 2 seconds, the angular velocity of the cylinder is 3t rad/s. Substituting t = 2 s, we get

ω = 3(2) = 6 rad/s

Therefore, the best choice is C, 14 rad/s, since it is the only option close to 6 rad/s.

A Solid Cylinder Has a Moment of Inertia of 2 τ\tauτ