A turntable of moment of inertia 0.30 kg·m² is spinning ccw
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A turntable of moment of inertia 0.30 kg·m² is spinning ccw. At t = 0 its angular momentum is +1.2 kg·m²·s⁻¹.
Starting at t = 0 a variable external torque is applied according to the description below (ccw positive):
• 0 ≤ t ≤ 1.0 s: The torque increases linearly from 0 N·m at t = 0 to +4.0 N·m at t = 1.0 s.
• 1.0 s < t ≤ 3.0 s: The torque remains constant at +4.0 N·m.
• 3.0 s < t ≤ 5.0 s: The torque decreases linearly to −2.0 N·m at t = 5.0 s.
• 5.0 s < t ≤ 6.0 s: The torque stays constant at −2.0 N·m.
(a) Sketch the torque–versus–time graph for 0 ≤ t ≤ 6.0 s, labeling key values on both axes.
(b) Write algebraic expressions for the torque as a function of time in each of the four intervals defined above.
(c) Calculate the angular impulse delivered to the turntable in each interval and determine the net angular impulse from 0 to 6.0 s.
(d) Determine the turntable’s angular momentum and angular speed at t = 6.0 s.
(e) Compare the rotational kinetic energy of the turntable at t = 6.0 s with its value at t = 0 s, stating whether it is greater, less, or the same, and justify your answer quantitatively.