(a) The angular velocity of the disk can be found using the formula:
angular velocity (ω) = initial angular velocity + (angular acceleration * time)
Since the disk is initially at rest, the initial angular velocity is 0 rad/s. Plugging in the given values:
ω = 0 + (7.8 rad/s² * 4.0 s)
ω = 31.2 rad/s
So, the angular velocity of the disk at t = 4.0 s is 31.2 rad/s.
(b) To find the tangential acceleration at the edge of the disk, we can use the formula:
tangential acceleration (at) = radius * angular acceleration
Given that the radius (r) of the disk is 12 cm = 0.12 m, and the angular acceleration (α) is 7.8 rad/s²:
at = 0.12 m * 7.8 rad/s²
at = 0.936 m/s²
So, the tangential acceleration at the edge of the disk at t = 4.0 s is 0.936 m/s².
The centripetal acceleration (ac) at the edge of the disk is equal to the tangential acceleration since they both point towards the center of the circular motion. Therefore, ac = 0.936 m/s².
