Question

A person is riding a bicycle, and its wheels have an angular velocity of 26.0 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 17.6 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?

Do I need to convert revolutions to radians first?



Physics(Please respond) - Elena, Tuesday, June 5, 2012 at 11:31am
Equations for decelerated motion are
ù=ùₒ - å•t,
ö = ùₒ•t - å•t²/2.

Since ù =0, ö = 2•ð•N, where N =17.6 rev.
these equatuions are
0=ùₒ-å•t, …………………… (1)
2•ð•N = ùₒ•t - å•t²/2 …………(2)
From (1)
å = ùₒ/t……………………… (3)
Plug it in (2) and obtain
t= 4•ð•N/ ùₒ.
Then determine angular acceleration using (3).



so first I have to do equation 2? So
2*pi*17.6 = I am not sure what wo is. Would it be the 26.0?

Answer 1

ε = ωₒ/t
(3) ->(2)
2•π•N = ωₒ•t - ε•t²/2 = ωₒ• t – (ωₒ/t) •t²/2 = ωₒ• t/2,
t= 4•π•N/ ωₒ =4•π•17.6/26 =8.5 s
ε = ωₒ/t = 26/8.5=3.06 rad/s²