A rock stuck in the tread of a 50.0 cm diameter bicycle wheel has a tangential speed of 3.5 0m/s . When the brakes are applied, the rock's tangential deceleration is 1.40 m/s^2 .
What is the magnitudes of the rock's angular acceleration at = 1.70 ?
To find the magnitude of the rock's angular acceleration, we can use the following formula:
angular acceleration (α) = tangential acceleration (a) / radius (r)
However, we don't have the tangential acceleration directly in this problem. We are given the tangential speed and tangential deceleration.
To find the tangential acceleration, we can use the formula:
tangential acceleration (a) = change in tangential speed (Δv) / time (t)
We are not given the time, but we can find it using the information given.
The change in tangential speed can be calculated using the formula:
change in tangential speed (Δv) = final tangential speed (v_f) - initial tangential speed (v_i)
Given that the initial tangential speed (v_i) is 3.50 m/s and the final tangential speed (v_f) is 0 m/s (due to deceleration), we can calculate Δv.
Now, we can calculate the time using the formula:
time (t) = Δv / tangential deceleration (a)
Given that tangential deceleration (a) is 1.40 m/s^2, we can substitute the values and calculate the time.
Once we have the time, we can substitute the tangential acceleration and the radius (which is half the diameter) into the formula:
angular acceleration (α) = tangential acceleration (a) / radius (r)
Given that the diameter of the bicycle wheel is 50.0 cm, the radius is 25.0 cm (or 0.25 m).
Now, we can calculate the angular acceleration by substituting the values into our formula:
angular acceleration (α) = tangential acceleration (a) / radius (r)
Please note that to accurately answer this question, the units of all the variables must be consistent (e.g., meters or centimeters).