Question
For full points the answers must be correct.
The diagram shows a rope passing around a circular wheel. The values of the tensions in the rope are illustrated. Assume the rope does not slip relative to the wheel as the wheel rotates and use the convention that clockwise rotational variables are negative and counter-clockwise rotational variable are positive. If the diameter of the wheel is 0.6m, then the net torque acting on it is: -30Nm -42 Nm +12Nm -12Nm +42N If the moment of inertial of the wheel is 12 kg.m2, the angular acceleration of the wheel is: +3.5 rad s-2 -1 rad s-2 +1 rad s-2 +2.5 rad s-2 -2.5 rad s-2 The wheel is initially at rest when the net torque is applied. Which of the following statements about the magnitude of the angular momentum of the wheel is true? Assume the tensions do not change in magnitude or direction. It increases with time at a decreasing rate. It decreases with time at a steady rate. It increases with time at an increasing rate. It increases with time at a steady rate. None of A through D s true
Explanation / Answer
Part 1)
The net force is 90 - 50 = 40 N
Torque = Fr and r = .3m
Torque = (40)(.3) = 12 Nm - Choice C
Part 2)
Torque = Ia
12 = 12(a)
a = 1 rad/s^2 - Choice C
Part 3)
Since L = Iw
I stays the same, but w increases with time at a steady rate
Thus momentum will also increase with time at a steady rate - Choice D
