The angular speed of a rotating platform changes from ω0 = 3.6 rad/s to ω = 6.4 rad/s at a constant rate as the platform moves through an angle Δθ = 5.5 radians. The platform has a radius of R = 12 cm. Calculate the angular acceleration of the platform α in rad/s2.

An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: θ(t) = a + bt2 – ct3 where a = 2.1 rad, b = 0.75 rad/s2 and c = 0.035 rad/s3. a. Determine an equation for the angular speed of the ride as a function of time, omega(t). Write your answet using the symbols a, b, and c, instead of their numerical values. b. Besides at t = 0, at what time t1 is the ride stopped? Give your answer in seconds. c. What is the magnitude of the angular displacement of the ride in radians between times t = 0 and t = t1? d. Determine an equation for the angular acceleration of the ride as a function of time, alpha(t). Write your answer using the symbols a, b, and c, instead of their numerical values.  e. What is the angular acceleration in rad/s^2 when the ride is at rest t = t1?

The angular position of a rotating object is given by the equation 0 = a + bt + ct2 where a, b, and c are constants. Here a = 1.44 rad, b = 2.00 rad/s, and c = 3.06 rad/s2. (a) What is the position of the object at t1 = 0 and t2 = 4.00 s? 01 rad 02 rad (b) What is the angular speed of the object at t1 = 0 and t, = 4.00 s? %3D rad/s @2 = rad/s (c) What is the angular acceleration of the object at t, = 0 and t, = 4.00 s? a1 = rad/s? rad/s?

A ceiling fan is rotating counterclockwise with a constant angular acceleration of 0.40? rad/s2 about a fixed axis perpendicular to its plane and through its center. Assume the fan starts from rest.