A tire placed on a balancing machine in a service station starts from rest and turns through 4.93 revolutions in 1.47 s before reaching its final angular speed. Calculate its angular acceleration. It must be in units of radians.
Please help. I have 20 attempts to do this and I have already used 12...each time I do it a different way I get a completely different answer.
V = 4.93revs/1.47s * 6.28rad/rev = 21.1
rad/s = Angular velocity.
V = Vo + a*t
V = 21.1 rad/s.
Vo = 0
t = 1.47 s.
a = rad/s^2
Solve for a.
Oh boy, tire balancing can be a real spin! Let's try to figure this out together.
To find the angular acceleration, we need to use the formula:
Angular acceleration (α) = (final angular speed - initial angular speed) / time
First, we need to find the initial angular speed. Since the tire starts from rest, the initial angular speed is 0.
Now, let's find the final angular speed. We know that the number of revolutions is 4.93 and the time is 1.47 seconds. A full revolution is equivalent to 2π radians. So, 4.93 revolutions is 4.93 * 2π radians.
Final angular speed = (4.93 * 2π radians) / 1.47 seconds
Now that we have the initial and final angular speeds, we can calculate the angular acceleration:
Angular acceleration (α) = (final angular speed - initial angular speed) / time
Go ahead and plug in the values, and may the force be with you!
To find the angular acceleration of the tire, we need to use the equation:
angular acceleration (α) = ((final angular velocity - initial angular velocity) / time)
Given:
Number of revolutions = 4.93 revolutions
Time = 1.47 s
First, let's convert the number of revolutions to radians:
1 revolution = 2π radians
Therefore, 4.93 revolutions = 4.93 * 2π radians.
Now, let's calculate the initial and final angular velocities:
The initial angular velocity is zero since the tire starts from rest.
The final angular velocity is the angular displacement divided by time:
final angular velocity = (angular displacement / time)
final angular velocity = (4.93 * 2π radians / 1.47 s)
Next, let's plug the values into the equation for angular acceleration:
angular acceleration (α) = (final angular velocity (ω) - initial angular velocity (ω₀)) / time
angular acceleration (α) = (4.93 * 2π radians / 1.47 s - 0) / 1.47 s
Now, calculate the angular acceleration:
α = (4.93 * 2π) / 1.47 s
As you have mentioned, the answer must be in radians, so the units cancel, and the angular acceleration is:
α ≈ 20.938 radians/s²
Therefore, the angular acceleration of the tire is approximately 20.938 radians/s².
To calculate the angular acceleration of the tire, we can use the following formula:
angular acceleration (α) = (final angular velocity - initial angular velocity) / time
First, we need to find the initial and final angular velocities.
From the given information, we know that the tire starts from rest and turns through 4.93 revolutions in 1.47 seconds. Since one revolution is equal to 2π radians, we can convert the number of revolutions to radians:
4.93 revolutions * 2π radians/revolution = 31.01π radians
The final angular velocity can be calculated using the formula:
final angular velocity (ω) = change in angle / change in time
In this case, the change in angle is 31.01π radians, and the change in time is 1.47 seconds. Substitute these values into the formula to find the final angular velocity.
final angular velocity (ω) = 31.01π radians / 1.47 seconds = 21.15π radians/seconds
Now, we need to find the initial angular velocity. Since the tire starts from rest, the initial angular velocity is zero.
Substituting the values into the formula for angular acceleration:
angular acceleration (α) = (final angular velocity - initial angular velocity) / time
= (21.15π radians/seconds - 0) / 1.47 seconds
= 21.15π radians/seconds / 1.47 seconds
By dividing 21.15π radians/seconds by 1.47 seconds:
angular acceleration (α) ≈ 14.39 radians/seconds²
Therefore, the angular acceleration of the tire is approximately 14.39 radians/seconds².