Final answer:
In this problem, we are given the initial angular velocity and angular acceleration of a disk and we need to find its angular velocity at a given time, the angle it has rotated through, and the tangential acceleration of a point on the disk.
Step-by-step explanation:
To solve this problem, we need to use the equations of rotational motion. Let's go step by step:
a) We can find the angular velocity of the disk at t = 5.0 s using the equation:
angular velocity (w) = initial angular velocity (w0) + angular acceleration (alpha) * time (t)
Plugging in the values, we get:
w = 2.0 rad/s + (1.0 rad/s²)(5.0 s) = 2.0 rad/s + 5.0 rad/s = 7.0 rad/s
b) To find the angle the disk has rotated through during this time, we can use the equation:
angle (theta) = initial angular velocity (w0) * time (t) + 0.5 * angular acceleration (alpha) * time (t)²
Plugging in the values, we get:
theta = (2.0 rad/s)(5.0 s) + 0.5(1.0 rad/s²)(5.0 s)² = 10.0 rad + 0.5(1.0 rad/s²)(25.0 s²) = 10.0 rad + 0.5 rad = 10.5 rad
c) To find the tangential acceleration of a point on the disk at t = 5.0 s, we can use the equation:
tangential acceleration (a) = radius of the disk (r) * angular acceleration (alpha)
Plugging in the values, we get:
a = (0.10 m)(1.0 rad/s²) = 0.10 m/s²