A flywheel rotates at a constant angular acceleration. At time t = 1.38 s, it rotates with a speed of ω = 2.40 rad/s
in the clockwise direction. At time t = 5.97 s, it rotates with a speed of ω = 2.40 rad/s in the counter-clockwise
direction. What is its angular displacement from t = 0.00 s to t = 7.00 s? What is the tangential acceleration of apoint on the flywheel 0.223 m from the axis?
To find the angular displacement of the flywheel from t = 0.00 s to t = 7.00 s, we need to calculate the change in its angular position.
1. Calculate the initial angular position (θi) at t = 0.00 s.
Since no information about the initial position is given, we can assume θi = 0 rad.
2. Calculate the angular position (θ1) at t = 1.38 s.
Using the equation: ω = ωi + αt,
where ω is the final angular velocity, ωi is the initial angular velocity, α is the angular acceleration, and t is the time,
we can rearrange the equation to find the angular position:
θ1 = θi + ωit + (1/2)αt^2.
Given:
ωi = 0 rad/s (Since at t = 0.00 s, the initial speed is not given),
ω1 = 2.40 rad/s,
t = 1.38 s.
Plugging the values into the equation, we get:
θ1 = 0 + (0)(1.38) + (1/2)α(1.38)^2,
2.40 = 0 + (1/2)α(1.38)^2.
Solve for α:
α = (2.40 * 2) / (1.38)^2.
3. Calculate the angular position (θ2) at t = 5.97 s.
Using the same equation and the given values:
θ2 = θ1 + ω1(t - t1) + (1/2)α(t - t1)^2.
Given:
ωi = 0 rad/s (Since at t = 0.00 s, the initial speed is not given),
ω2 = -2.40 rad/s (since it is rotating in the opposite direction),
t = 5.97 s,
t1 = 1.38 s,
α is the value calculated in step 2.
Plugging the values into the equation, we get:
θ2 = θ1 + (2.40)(5.97 - 1.38) + (1/2)α(5.97 - 1.38)^2.
4. Calculate the angular displacement (Δθ).
Δθ = θ2 - θi.
Plugging the calculated values into the equation, we get the angular displacement from t = 0.00 s to t = 7.00 s.
To find the tangential acceleration of a point on the flywheel 0.223 m from the axis, we can use the equation: at = α * r,
where α is the angular acceleration and r is the distance from the axis of rotation. Using the value of α calculated in step 2 and r = 0.223 m, we can calculate the tangential acceleration.