A rotating object starts from rest at t = 0 s and has a constant angular acceleration. At a time of t = 7.0 s the object has an angular velocity of ω = 16 rad/s. What is its angular velocity at a time of t = 14 s?
40
Hay your answer is miserable, next time try giving how you did it
To find the angular velocity at t = 14 s, we can use the angular acceleration and the given initial conditions.
Given:
Initial angular velocity ω_0 = 0 rad/s (as the object starts from rest)
Angular acceleration α (constant)
Time t = 7.0 s, the object has an angular velocity ω = 16 rad/s
Using the equation:
ω = ω_0 + α * t
we can rearrange the equation to solve for α:
α = (ω - ω_0) / t
Substituting the given values:
α = (16 rad/s - 0 rad/s) / 7.0 s
= 16 rad/s / 7.0 s
≈ 2.286 rad/s^2
Now, we can use the equation:
ω = ω_0 + α * t
to find the angular velocity at t = 14 s:
ω = ω_0 + α * t
ω = 0 rad/s + (2.286 rad/s^2) * 14 s
ω ≈ 31.9 rad/s
Therefore, the angular velocity at t = 14 s is approximately 31.9 rad/s.
To find the angular velocity at t = 14 s, we can use the kinematic equation for rotational motion:
ω = ω0 + αt
where:
ω is the final angular velocity,
ω0 is the initial angular velocity (at t = 0 s),
α is the angular acceleration, and
t is the time elapsed.
Given that the object starts from rest (ω0 = 0) and has a constant angular acceleration, we can rearrange the equation to solve for the final angular velocity:
ω = αt
Since α is constant, we can use the given information to find its value. At t = 7.0 s, the angular velocity is ω = 16 rad/s. Substituting the values into the equation:
16 rad/s = α × 7.0 s
Now we can solve for α:
α = 16 rad/s / 7.0 s
α ≈ 2.29 rad/s²
Finally, we can find the angular velocity at t = 14 s by substituting the values into the initial equation:
ω = αt
ω = 2.29 rad/s² × 14 s
ω ≈ 32.06 rad/s
Therefore, the angular velocity at t = 14 s is approximately 32.06 rad/s.