A tire placed on a balancing machine in a service station starts from rest and turns through 10.8 revolutions in 8.48 s before reaching its final angular speed. Calculate its angular acceleration.

To find the angular acceleration, we need to use the formula:

Angular acceleration (α) = (Final angular velocity (ωf) - Initial angular velocity (ωi)) / Time (t)

We already have the values for time (t) and the number of revolutions made (10.8). However, we need to convert the unit of angular velocity from revolutions to radians, as angular acceleration is typically measured in radians per second squared.

Since one revolution is equal to 2π radians, we can convert the number of revolutions to radians using the following equation:

Angular displacement (θ) = Number of revolutions (n) * 2π

Now, let's calculate the initial angular velocity (ωi) and the final angular velocity (ωf) in radians per second.

Initial angular velocity (ωi) = 0 (since the tire starts from rest)

Final angular displacement (θf) = 10.8 revolutions * 2π radians/revolution

Final angular velocity (ωf) = Final angular displacement (θf) / Time (t)

Now we can substitute these values into the formula for angular acceleration:

Angular acceleration (α) = (Final angular velocity (ωf) - Initial angular velocity (ωi)) / Time (t)

Let's calculate the angular acceleration step by step:

1. Convert the number of revolutions to radians:
θf = 10.8 revolutions * 2π radians/revolution

2. Calculate the final angular velocity:
ωf = θf / t

3. Calculate the angular acceleration:
α = (ωf - ωi) / t

Let's plug in the values and solve for the angular acceleration.

displacement= 1/2 angulare acceleration*t^2

solve fodr angular acceleration