Question

which of the disks have positive angular acceleration? write down the numbers, in order, that correspond to the disk(s) that you believe meet this criteria, without commas or spaces between them. for example, if you think that the yellow disk and the gray disk are the correct ones, then you should enter 15.

Answer 1

Using rotational kinematics formulas, the angular velocity, swept angle, and tangential acceleration of a constantly accelerating disk can be calculated using the initial conditions and the time elapsed.

Step-by-step explanation:

Angular Acceleration and Kinematics of Rotational Motion

For a disk with constant angular acceleration, you can use the rotational kinematics formulas to solve for various quantities. Given a constant angular acceleration (α), the angular velocity (ω) at any time (t) can be found using the equation ω = ω0 + αt, where ω0 is the initial angular velocity. The angle (θ) swept by the disk in time t, given a constant angular acceleration, is found using θ = ω0t + (1/2)αt². In addition, the tangential acceleration (at) of a point on the edge of the disk is the product of the angular acceleration and the radius (r) of the disk, at = αr.

For example, a disk with an initial angular velocity of 2.0 rad/s and an angular acceleration of 1.0 rad/s² will have an angular velocity of 7.0 rad/s after 5 seconds and will have swept an angle of 22.5 radians (360° is approximately 6.28 radians) during that time. The tangential acceleration at the edge of the disk will be 10 m/s² if radius is 10 cm (0.1 m).