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
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To calculate the angular acceleration of the tire, we need to use the formula:
Angular acceleration (α) = (Final angular velocity - Initial angular velocity) / Time
Given:
- The tire starts from rest, which means its initial angular velocity (ωi) is 0.
- The tire turns through 4.82 revolutions, which is equivalent to 4.82 * 2π radians.
- The time taken is 1.48 seconds.
First, we need to convert the revolution into radians:
4.82 revolutions * 2π radians/revolution = 4.82 * 2π radians
Next, we can substitute the values into the formula:
Angular acceleration (α) = (Final angular velocity - Initial angular velocity) / Time
= (Final angular velocity - 0) / 1.48
Now, we need to find the final angular velocity (ωf). We know that angular velocity is given by the formula:
Angular velocity (ω) = (2π * number of revolutions) / time
So, we can rearrange the formula to solve for the final angular velocity:
Final angular velocity (ωf) = (2π * 4.82) / 1.48
Finally, we can substitute the final angular velocity into the original formula to find the angular acceleration:
Angular acceleration (α) = (Final angular velocity - 0) / 1.48
Now, you can calculate the angular acceleration by plugging in the values in the equations and performing the necessary calculations.
displacment=1/2 acceleration*t^2
displacement=4.82*2PI radians
solve for acceleration.