To find the time taken for the bike to come to rest, we can use the formula:
time = angular displacement / angular velocity
In this case, the angular displacement is given in revolutions, so we need to convert it to radians. Since one revolution is equivalent to 2Ï€ radians, the angular displacement is:
angular displacement = 16.0 revolutions * 2Ï€ radians/revolution
Now we can calculate the time:
time = (16.0 revolutions * 2Ï€ radians/revolution) / 24.0 rad/s
Simplifying the calculation:
time = (16.0 * 2Ï€) / 24.0 s
Therefore, the time taken for the bike to come to rest is:
time = 10.66 s (rounded to two decimal places)
Moving on to the second question, we can calculate the angular acceleration using the formula:
angular acceleration = (final angular velocity - initial angular velocity) / time
Since the bike comes to rest, the final angular velocity is zero. The initial angular velocity is given as +24.0 rad/s, and we have calculated the time as 10.66 s.
Now we can calculate the angular acceleration:
angular acceleration = (0 rad/s - 24.0 rad/s) / 10.66 s
Simplifying the calculation:
angular acceleration = -24.0 rad/s / 10.66 s
Therefore, the angular acceleration of each wheel is:
angular acceleration = -2.25 rad/s^2 (rounded to two decimal places)