Question

1) The flywheel of a steam engine begins to rotate from rest with a constant angular acceleration of 1.23 rad/s². It accelerates for 22.7 s, then maintains a constant angular velocity. Calculate the total angle through which the wheel has turned 57.7 s after it begins rotating. Hint:This is rotational motion, with equations for angles similar to those for linear motion. Note that the TOTAL time is given. Answer: ______ deg.

2) A proposed space station includes living quarters in a circular ring 52.5 m in diameter. At what angular speed should the ring rotate so the occupants feel that they have the same weight as they do on Earth? Hint: We assume that everyone lives at the given diameter. The rotation is around an axis through the center and perpendicular to the circle. Answer: ______ rad/s

3) A point on the rim of a 0.70 m diameter grinding wheel changes speed uniformly from 12 m/s to 20 m/s in 9.1 s. What is the average angular acceleration of the wheel during this interval? Answer: ________ rad/s^2

Answer 1

for first 22.7 s

theta = wi*t + 1/2*alpha*t^2

wi = 0

theta = alpha*t^2/2

theta = 316.9 rad

after 22.7 its moving constant angular velocity

wf = wi + alpha*t

wf = 1.23 * 22.7 = 27.921 rad/s

for next 35 sec

theta = wf*t

theta = 977.235 rad

total = 977.235 + 316.9 = 1294.135 rad

= 74148.47 degree

part 2 )

v^2/r = g

v = wr

w^*r = g

w = sqrt(g/r)

w = 0.611 rad/s

part 3 )

alpha = a/r

a = linear accelearation

a = vf-vi/t

a = 20 -12 /9.1

a = 8/9.1

alpha = a/r

r = 0.35 m

alpha = 2.51 rad/s^2