Yes, in order to calculate the time taken for the bike to come to rest and the angular acceleration of each wheel, you will need to convert the given angular displacement from revolutions to radians.
To convert from revolutions to radians, you can use the conversion factor:
1 revolution = 2Ï€ radians
So, in this case, where the angular displacement is given in revolutions, you can convert it to radians by multiplying it by 2Ï€.
Now, let's solve the problem.
(a) To find the time taken for the bike to come to rest, you can use the formula:
Time = Angular displacement / Angular velocity
The given angular displacement is 17.6 revolutions, which we can convert to radians by multiplying it by 2Ï€:
Angular displacement in radians = 17.6 revolutions * 2Ï€ radians/revolution
(b) To find the angular acceleration of each wheel, you can use the formula:
Angular acceleration = (Final angular velocity - Initial angular velocity) / Time
The final angular velocity is 0 rad/s since the bike comes to a stop. The initial angular velocity is given as 26.0 rad/s.
Now, let's calculate the answers:
(a) Convert revolutions to radians:
Angular displacement in radians = 17.6 revolutions * 2Ï€ radians/revolution
(b) Angular acceleration:
Angular acceleration = (0 rad/s - 26.0 rad/s) / Time
So, to answer your question, yes, you need to convert the given angular displacement from revolutions to radians in order to solve this problem.