A tire placed on a balancing machine in a service station starts from rest and turns through 4.82 revolutions in 1.48 s before reaching its final angular speed. Calculate its angular acceleration.
To calculate the angular acceleration, we need to use the following equation:
angular acceleration (α) = (final angular speed - initial angular speed) / time
Given:
Initial angular speed (ω0) = 0 (as the tire starts from rest)
Final angular speed (ω) = ?
Time (t) = 1.48 s
Number of revolutions (n) = 4.82
First, let's find the final angular speed (ω):
Since the tire turns through 4.82 revolutions in 1.48 seconds, we can calculate the angle covered:
angle (θ) = 2πn = 2π(4.82) = 30.289 radians
Next, we can calculate the final angular speed (ω):
ω = θ / t = 30.289 rad / 1.48 s = 20.54 rad/s
Now, we can calculate the angular acceleration (α):
α = (ω - ω0) / t
= (20.54 rad/s - 0) / 1.48 s
≈ 13.89 rad/s^2
Therefore, the angular acceleration of the tire is approximately 13.89 rad/s^2.