A car leaves an intersection after a light turns green. It starts from rest and reaches a speed of 13.4 m/s in 5.0 s. The radius of a tire of the car is 0.25 mDetermine the average rotational acceleration of the tire.
find acceleration by dividing 13.4 m/s by 5.0 s. the divide by the radius, .25m
acceleration=changespeed/time=13.4/5 m/s^2
alpha=acceleration/radius=above/.25
=4*13.4/5 rad/sec^2
average, divide by 2, or wavg=2/5*13.4 rad/sec^2
To determine the average rotational acceleration of the tire, we can use the formula:
average rotational acceleration = (final angular velocity - initial angular velocity) / time
However, to use this formula, we need to find the initial and final angular velocities.
First, let's find the initial angular velocity:
Since the car starts from rest, the initial angular velocity is zero.
Next, let's find the final angular velocity:
The final angular velocity can be determined using the formula: final angular velocity = linear velocity / radius
Given that the linear velocity of the car is 13.4 m/s and the radius of the tire is 0.25 m, we can substitute these values into the formula:
final angular velocity = 13.4 m/s / 0.25 m = 53.6 rad/s
Now, we can substitute the values into the formula for average rotational acceleration:
average rotational acceleration = (53.6 rad/s - 0 rad/s) / 5.0 s = 10.72 rad/s^2
Therefore, the average rotational acceleration of the tire is 10.72 rad/s^2.
To determine the average rotational acceleration of the tire, we need to calculate the angular acceleration (α) first. Here's how you can do that step-by-step:
1. Convert the linear velocity to angular velocity:
The linear velocity of the car is given as 13.4 m/s. The linear velocity of a point on the edge of the tire is the same as the speed of the car. We can convert this linear velocity to angular velocity using the formula:
Angular velocity (ω) = Linear velocity / Radius
Given that the radius of the tire is 0.25 m, we can calculate the angular velocity as:
ω = 13.4 m/s / 0.25 m
2. Calculate the change in angular velocity:
The car starts from rest, so initially, the angular velocity is zero. We need to find the change in angular velocity (∆ω) over the given time period of 5.0 seconds.
∆ω = Final angular velocity - Initial angular velocity
= ω - 0
3. Determine the angular acceleration:
The average rotational acceleration (α) can be obtained using the formula:
α = ∆ω / ∆t
Given that the time period is 5.0 seconds, we can calculate the angular acceleration as:
α = ∆ω / 5.0 s
Now, plug in the values and calculate the average rotational acceleration.