Please let me know if there are places where I am unclear, or you think I am incorrect -- I do make arithmetic and typing mistakes ...
1. Use theta = theta0 + omega0 * t + 0.5 *
alpha * t ^2
Recall that CW is negative! so (theta - theta0) and omega0 are both
negative ...
the answer you should get is 1.09 rad/s2 CCW.
Note: if you made CW positive (by not using the negative sign above),
your angular acceleration will be negative -- meaning opposite the original
angular velocity ==> "slowing down".
2. (a) I used v2 = v02
+ 2a*(y - y0) and calculated a = 4.5 cm/s2 UP =>
slowing down, as expected.
(b) since m1 is moving down, the wheel is rotating CCW, and omega
= tangential velocity 1 / R1,
so omega = 15 cm/s / 2 cm = 7.5 rad/s
(c) radial acceleration = centripetal acceleration = v2 / R = omega2
R = (7.5 rad/s)^2 (5 cm)
= 2.81 m/s2 towards
the center of the wheel
Note: I assumed the edge meant the outside of the whole
wheel at 5 cm.
(d) the angular acceleration, alpha = tangential component of linear acceleration
/ R, so
alpha = [ans to (a)] / R1 = 4.5 cm/s2 / 2 cm =
2.25 rad/s2 CW
(e) v2 = omega * R2 = 7.5 rad/s * 5 cm = 37.5 cm/sec DOWN
(f) arc length s = R * theta in radians and the arclength traveled
by the wheel is equal to the linear distance traveled by each of the masses,
so
theta = s1 / R1 = 25 cm / 2 cm = 12.5 radians
Note: this is about 2 revolutions.
(g) for m2, it has the same theta, but a different R, so
s2 = R2 * theta = 5 cm * 12.5 radians = 62.5 cm
This page maintained by Anne G. Young. Last modified 11-Mar-2005 .