car has tires of radius 25 cm. The car accelerates from rest at a constant rate of 2.0m/s/s find angular acceleration. find angular displacement. how many revolutions is this?
To find the angular acceleration, we first need to convert the linear acceleration of the car from m/s^2 to cm/s^2, as the radius of the tires is given in centimeters.
Given:
Radius of the tires (r) = 25 cm
Linear acceleration (a) = 2.0 m/s^2
First, we convert the linear acceleration to cm/s^2:
1 m = 100 cm
So, 2.0 m/s^2 = 2.0 * 100 cm / s^2 = 200 cm/s^2
The linear acceleration of the car is 200 cm/s^2.
Next, let's find the angular acceleration.
Angular acceleration (α) can be calculated using the following formula:
α = a / r
Plugging in the values, we have:
α = 200 cm/s^2 / 25 cm
α = 8.0 rad/s^2
Therefore, the angular acceleration of the car is 8.0 rad/s^2.
Now let's find the angular displacement.
To do this, we need to know the time for which the car accelerates. Without the time provided, we cannot compute the angular displacement accurately.
Finally, let's calculate how many revolutions this angular displacement corresponds to.
To find the number of revolutions, we need to know the total angular displacement and the circumference of a circle with the given radius.
Revolutions (N) can be calculated using the following formula:
N = (θ / 2π)
θ - Angular displacement in radians
2π - The full revolution in radians (360 degrees)
Since we don't have the angular displacement, we cannot determine the number of revolutions without additional information.
In conclusion, we were able to find the angular acceleration but could not determine the angular displacement or the number of revolutions without the time or additional information.