A 0.125 kg meter stick is rota ting (as shown to the right) in a horizontal plan
ID: 1516185 • Letter: A
Question
A 0.125 kg meter stick is rota ting (as shown to the right) in a horizontal plane about an axis 15.0 cm from its end at 3.45 rad/s. a) Find its rotational inertia. b) Find the speed of the end farthest from the axis of rotation. c) Find the radial acceleration of the end farthest from t he axis of rotation. If this stick comes to rest in 4.72 s, find its d) angular acceleration, e) tangential acceleration, and f) the net torque acting on it as it slows down. g) If this net torque is generated by a single force directed perpendicular to an d out of the page at 15.0 cm from the end of the stick opposite to the axis, determine the magnitude of this force.
Explanation / Answer
a) Use Parallel axis theorem,
I = Icm + m*d^2
= m*L^2/12 + m*(L/2 - 0.15)^2
= 0.125*1^2/12 + 0.125*(1/2 - 0.15)^2
= 0.02573 kg.m^2
f) angular acceleration, alfa = dw/dt
= 3.45/4.72
= 0.7309 rad/s^2
net torque acting on it, Tnet = I*alfa
= 0.02573*0.7309
= 0.0188 N.m
g) Tnet = F*r*sin(90)
F = Tnet/r
= 0.0188/0.15
= 0.1254 N
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