A 44.3-cm diameter disk rotates with a constant angular acceleration of 2.3 rad/s2. It starts from rest at t = 0, and a line drawn from the center of the disk to a point P on the rim of the disk makes an angle of 57.3° with the positive x-axis at this time.
(a) Find the angular speed of the wheel at t = 2.30 s.
w=wi+alpha*t
wi=0
alpha = 2.3rad/s^2
t=2.3sec
solve for w.
To find the angular speed of the wheel at t = 2.30 s, we need to use the equations of rotational motion. The equation that relates the angular speed (ω), initial angular speed (ω0), angular acceleration (α), and time (t) is:
ω = ω0 + αt
In this case, the initial angular speed (ω0) is 0 rad/s since the disk starts from rest. The angular acceleration (α) is given as 2.3 rad/s^2. The time (t) is given as 2.30 s.
Plugging in the given values, we get:
ω = 0 + (2.3 rad/s^2)(2.30 s)
= 5.29 rad/s
Therefore, the angular speed of the wheel at t = 2.30 s is 5.29 rad/s.