A thin, uniform rod of length 1.2 m and mass 4.0 kg is pivoted about its center so it can rotate freely in a horizontal plane. The rod is initially at rest. A student in a physics lab performs the following sequence:
• From t = 0 to t = 1.0 s, an external torque of 3.0 N·m is applied clockwise.
• From t = 1.0 s to t = 3.0 s, a different device applies a constant external torque of 2.0 N·m counter-clockwise.
No other significant torques act on the rod during this 3-s experiment.
(a) Show that the moment of inertia of the rod about the pivot is 0.48 kg·m².
(b) Determine the angular speed of the rod (magnitude and direction) at t = 1.0 s.
(c) Determine the angular speed of the rod (magnitude and direction) at t = 3.0 s.
(d) On axes whose time scale matches the experiment, sketch qualitative graphs of angular velocity ω(t) and angular momentum L(t) for 0 ≤ t ≤ 3.0 s, labeling key values from your calculations.