posted by Maggie on .
A person is riding a bicycle, and its wheels have an angular velocity of 17.7 rad/s. Then, the brakes are applied and the bike is brought to a uniform stop. During braking, the angular displacement of each wheel is 12.4 revolutions. (a) How much time does it take for the bike to come to rest? (b) What is the anguar acceleration (in rad/s2) of each wheel?
w = w0 - a*t
theta = theta0 + w0*t - 1/2*a*t^2
where w is the angular velocity as a function of time, w0 is the initial velocity, t is time, a is the angular acceleration, theta is the angular displacement, and theta0 is the initial angular displacement.
12.4 revolutions = 2*pi*12.4 radians
when the bike stops, w = 0. Inserting values into the equation:
0 = 17.7 - a*t
2*pi*12.4 = 17.7*t - .5*a*t^2
Use algebra to solve this system of equations to find the time t that it takes the bike to come to rest, and the angular acceleration a.