Physics

Problem

A thin ring of radius

0.25\,\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\,\text{s}

t = 2\,\text{s}

\alpha = +1.8\,\text{rad/s}^2

(constant). • From

t = 2\,\text{s}

t = 5\,\text{s}

\alpha = 0\,\text{rad/s}^2

. • From

t = 5\,\text{s}

t = 7\,\text{s}

\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. a. Part 1: (a) Determine the ring’s angular velocity at

t = 2\,\text{s}

t = 5\,\text{s}

, and

t = 7\,\text{s}

. b. Part 2: (b) Calculate the particle’s linear speed at the instant

t = 5\,\text{s}

. c. Part 3: (c) Find the maximum linear speed attained by the particle during the entire

7\,\text{s}

interval and specify when it occurs. d. Part 4: (d) Compute the total linear displacement of the particle from

t = 0\,\text{s}

t = 7\,\text{s}

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