A person is riding a bicycle, the wheels of a bicycle have an angular velocity of +24.0 rad/s. Then, the brakes are applied. In coming to rest, each wheel makes an angular displacement of +16.0 revolutions.
(a) How much time does it take for the bike to come to rest?
s
(b) What is the angular acceleration of each wheel?
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 2π radians, the angular displacement is:
angular displacement = 16.0 revolutions * 2π radians/revolution
Now we can calculate the time:
time = (16.0 revolutions * 2π radians/revolution) / 24.0 rad/s
Simplifying the calculation:
time = (16.0 * 2π) / 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)