Final answer:
The angular acceleration is π/4 rad/s². The tangential acceleration of the rim is π/8 m/s².
Step-by-step explanation:
A) Find the angular acceleration:
Angular acceleration is the rate of change of angular velocity. It can be calculated using the formula:
Angular acceleration = (Final angular velocity - Initial angular velocity) / Time
Given that the flywheel speeds up uniformly from rest to 900 rpm in 2 minutes, we can convert the final angular velocity from rpm to rad/s:
Final angular velocity = 900 rpm * (2π rad/1 min) * (1 min/60 s) = 30π rad/s
Initial angular velocity is 0 rad/s.
Therefore, the angular acceleration is:
Angular acceleration = (30π rad/s - 0 rad/s) / 120 s = π/4 rad/s².
B) Find the tangential acceleration of the rim:
Tangential acceleration is the acceleration along the tangent of the circular path. It can be calculated using the formula:
Tangential acceleration = Radius * Angular acceleration
Given that the radius of the flywheel is 0.5 m and the angular acceleration is π/4 rad/s², we can calculate:
Tangential acceleration = 0.5 m * (π/4 rad/s²) = π/8 m/s².