Question

A bicycle wheel has an initial angular velocity of 1.5 rad/sec. Its angular acceleration is constant and equal to 0.2 rad/sec².

a) What is the angular velocity after it has turned through 3.5 revolutions?

b) How long does it take for the wheels to reach this angular position?

c) Find the average velocity.

Answer 1

a.)

from rotational kinematics third law,

wf^2 - wi^2 = 2**

given, wi = initial angular velocity = 1.5 rad/sec.

wf = final angular velocity = ??

= angular acceleration = 0.2 rad/s^2

= rotation = 3.5 rev = 3.5*2*pi = 22 rad

So, wf = sqrt(1.5^2 + 2*0.2*22)

wf = 3.32 rad/sec.

b.)

from rotational kinematics first law,

wf - wi = *t

given, wi = initial angular velocity = 1.5 rad/sec.

wf = final angular velocity = 3.32

t = time = ??

So, t = (wf - wi)/ = (3.32-1.5)/0.2

t = 9.1 sec.

c.)

average velocity(w_avg) = (total rotation)/time = 22/9.1

w_avg = 2.42 rad/sec.

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