A wheel starts from rest and rotates about its axis with constant angular acceleration. After 8.7s have elapsed, it has rotated through an angle of 20 radians.
What is the angular acceleration of the wheel?
What is the angular velocity when the time t = 8.7 s? I got the answer of 4.60 rad/s
What is the centripetal acceleration of a point on the wheel a distance r = 0.25 m from the axis at t = 8.7 s?
20 rad/s^2
4 rad/s
10 rad/s^2
To find the angular acceleration of the wheel, we can use the formula:
θ = 0.5 * α * t^2
where θ is the angle rotated, α is the angular acceleration, and t is the time. Rearranging the formula, we get:
α = (2 * θ) / t^2
Plugging in the values given, we have:
α = (2 * 20 radians) / (8.7s)^2
α ≈ 0.487 rad/s^2
So, the angular acceleration of the wheel is approximately 0.487 rad/s^2.
To find the angular velocity at t = 8.7s, we can use the formula:
ω = ω0 + α * t
where ω is the final angular velocity, ω0 is the initial angular velocity (which is 0 since the wheel starts from rest), α is the angular acceleration, and t is the time. Plugging in the values given, we have:
ω = 0 + (0.487 rad/s^2) * (8.7s)
ω ≈ 4.24 rad/s
So, the angular velocity when t = 8.7s is approximately 4.24 rad/s.
To find the centripetal acceleration of a point on the wheel at t = 8.7s, we can use the formula:
ac = r * α
where ac is the centripetal acceleration, r is the distance from the axis, and α is the angular acceleration. Plugging in the values given, we have:
ac = (0.25m) * (0.487 rad/s^2)
ac ≈ 0.12 m/s^2
So, the centripetal acceleration of a point on the wheel at t = 8.7s is approximately 0.12 m/s^2.