Starting from rest, a disk rotates about its central axis with constant angular acceleration. In 7.00 s, it rotates 18.8 rad. During that time, what are the magnitudes of (a) the angular acceleration and (b) the average angular velocity? (c) What is the instantaneous angular velocity of the disk at the end of the 7.00 s? (d) With the angular acceleration unchanged, through what additional angle (rad)

A wheel 1.4 m in diameter rotates with an angular acceleration of 2.0 rad/s. (Enter the magnitudes.) (a) If the wheel's initial angular velocity is 5.0 rad/s, what is its angular velocity (in rad/s) after 10 s? rad/s (b) Through what angle (in rad) does it rotate in the 10 s interval? rad (c) What are the tangential speed (in m/s) and tangential acceleration (in m/s2) of a point on the rim of the wheel at the end of the 10 s interval? tangential speed m/s tangential acceleration m/s2

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 disk 8.08 cm in radius rotates at a constant rate of 1 150 rev/min about its central axis. (a) Determine its angular speed. X Note that 1150 rev/min is an angular speed, but the problem asks for different units. rad/s (b) Determine the tangential speed at a point 3.02 cm from its center. What is the relationship between angular speed and tangential speed? m/s (c) Determine the radial acceleration of a point on the rim. magnitude direction Note that the radial acceleration is also called centripetal acceleration. km/s² toward the center (d) Determine the total distance a point on the rim moves in 1.96 s. × You appear to have correctly calculated this distance using your incorrect value from part (b). m