Rotational Velocity & Acceleration Practice Problems

The angular position of a small sphere welded on a spinner wheel is given in the graph below. Calculate the angular velocity at t = 5 s and t =10 s

The equation ω_z(t) = B - Dt² gives the angular velocity of a rotating particle, where B = 3.80 rad/s and D = 0.940 rad/s³. Determine the average angular acceleration for the interval t = 0 - 2.50 s and instantaneous angular acceleration when t = 2.50 s. α_av-z = ? α_z = ?

The equation ω_z(t) = C - Dt² gives the angular velocity of a rotating particle, where C = 4.20 rad/s and D = 0.250 rad/s³. Express its angular accleration in the form α(t) = ? 

A decoration on a rotating disk has angular velocity given by ω_z(t) = C + Dt² where C and D are constants and t is in seconds. The numerical values of C and D are 3.25 and 0.850 respectively. Determine the decoration's angular acceleration at t = 0 s and t = 3.60 s. 

A sphere follows a circular trajectory such that its angular position follows θ(t) = X + Yt - Zt³, where θ is measured in radians, t is measured in seconds, and X, Y, and Z are constants. At t = 0, the angular position of the X is θ = π/3 while the angular velocity is 1.30 rad/s. In another instance, t = 1.80 s, the sphere has an angular acceleration of 0.900 rad/s². At the moment where angular accleration is 2.80 rad/s², determine the values of angular velocity and angular position.

A toy Ferris wheel spins such that its angular position follows the equation θ(t) = X + Yt - Zt³, where θ is measured in radians, t is measured in seconds, and X, Y, and Z are constants. At t = 0, the angular position of the wheel is θ = π/5 while the angular velocity is 1.60 rad/s. At another instance of time, t = 1.40 s, the wheel has an angular acceleration of 1.30 rad/s². Determine the angular acceleration of the wheel at the moment when θ = π/5 rad.

A toy Ferris wheel spins such that its angular position follows the equation θ(t) = X + Yt - Zt³, where θ is measured in radians, t is measured in seconds, and X, Y, and Z are constants. At t = 0, the angular position of the wheel is θ = π/2 while the angular velocity is 1.70 rad/s. At another instance of time, t = 2.20 s, the wheel has an angular acceleration of 0.875 rad/s². Determine the values of  X, Y, and Z and indicate their units.