A cylinder of radius r = 0.4 m is about to start rolling down an inclined plane. The acceleration of the center of the cylinder is 9.81 sin(0) m/s². The angular acceleration is 9.81 sin(0)/r rad/s². Assume 0 = 0.2 rad. What is the magnitude of acceleration of the point on the cylinder furthest from the inclined plane in m/s². Hint: Since it is about to start rolling, the velocity of the center of the cylinder and angular velocity of the cylinder are still zero at that instant.

A small fan has blades that have a radius of 0.0600 m. When the fan is turned on, the tips of the blades have a tangential acceleration of 23.5 m/s2 as the fan comes up to speed. What is the angular acceleration α of the blades?

A disk of radius 2.25 m rotates about its axis. Points on the rim of the disk undergo tangential acceleration of magnitude 1.81 m/s?. At a particular time, the rim has a tangential speed of 1.67 m/s. At a time 0.867 s later, what is the tangential speed v of a point on the rim, the magnitude of the point's radial acceleration a,, and the magnitude of its total acceleration Arot? U = m/s ar = m/s? Atot = m/s?

The angular position as a function of time of a rotating cylinder is giving by: θ(t) = 2.50(rad/s2)t2 – 0.60(rad/s3)t3.  Find the maximum angular speed of the cylinder. Use calculus.

An engine flywheel initially rotates counterclockwise at 6.83 rotations/s. Then, during 25.1 s, its rotation rate changes to 2.19 rotations/s clockwise. Find the flywheel's average angular acceleration (including its sign) in radians per second squared. Define counterclockwise rotation as positive.   what is the average angular acceleration?

A wheel that is 34.0 cm in diameter rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s. What is the magnitude of the tangential (linear) acceleration of the wheel?

A wind turbine is rotating counterclockwise at 0.78 rev/s and slows to a stop in 21 s. Its blades are 27 m in length. (a) What is the angular acceleration of the turbine (in rad/s)? (Indicate the direction with the sign of your answer.) |rad/s2 (b) What is the centripetal acceleration (in m/s2) of the tip of the blades at t = 0? (Enter the magnitude. Round your answer to at least two decimal places.) m/s? (c) What is the magnitude (in m/s) of the total linear acceleration of the tip of the blades at t = 0? (Round your answer to at least two decimal places.) m/s2 What is the angle that this total linear acceleration vector makes with the centripetal acceleration vector? (Enter the magnitude of the smallest such angle in degrees.)

A platform is rotating with an angular speed of 3.00 rad/s and an angular acceleration of 11.0 rad/s². At a point on the platform that is 1.26 m from the axis of rotation, what is the magnitude of the total acceleration a?

A fan blade is rotating with a constant angular acceleration of + 9.9 rad/s2. At what point on the blade, as measured from the axis of rotation, does the magnitude of the tangential acceleration equal that of the acceleration due to gravity? r = i

A motorcycle accelerates uniformly from rest and reaches a linear speed of 26.8 m/s in a time of 9.80 s. The radius of each tire is 0.287 m. What is the magnitude of the angular acceleration of each tire?