A thin ring of radius is initially at rest

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

A thin ring of radius 0.25 m0.25\,\text{m} is initially at rest. The angular acceleration of the ring as a function of time is given by the following schedule: • From t=0 st = 0\,\text{s} to t=2 st = 2\,\text{s}, α=+1.8 rad/s2\alpha = +1.8\,\text{rad/s}^2 (constant). • From t=2 st = 2\,\text{s} to t=5 st = 5\,\text{s}, α=0 rad/s2\alpha = 0\,\text{rad/s}^2. • From t=5 st = 5\,\text{s} to t=7 st = 7\,\text{s}, α=−2.4 rad/s2\alpha = -2.4\,\text{rad/s}^2 (constant). Respond to the tasks below concerning a dust particle that adheres to the outer edge of the ring. (1) Part 1: (a) Determine the ring’s angular velocity at t=2 st = 2\,\text{s}, t=5 st = 5\,\text{s}, and t=7 st = 7\,\text{s}. (2) Part 2: (b) Calculate the particle’s linear speed at the instant t=5 st = 5\,\text{s}. (3) Part 3: (c) Find the maximum linear speed attained by the particle during the entire 7 s7\,\text{s} interval and specify when it occurs. (4) Part 4: (d) Compute the total linear displacement of the particle from t=0 st = 0\,\text{s} to t=7 st = 7\,\text{s}.

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