1) A string trimmer is a tool for cutting grass and weeds; it utilizes a length...

1) A string trimmer is a tool for cutting grass and weeds; it utilizes a length of nylon "string" that rotates about an axis perpendicular to one end of the string. The string rotates at an angular speed of 47 rev/s, and its tip has a tangential speed of 56 m/s. What is the length of the rotating string?

2) A planet orbits a star, in a year of length 4.62 x 10⁷ s, in a nearly circular orbit of radius 3.87 x 10¹¹ m. With respect to the star, determine (a) the angular speed of the planet, (b) the tangential speed of the planet, and (c) the magnitude of the planet's centripetal acceleration.

3) A star has a mass of 1.56 x 10³⁰ kg and is moving in a circular orbit about the center of its galaxy. The radius of the orbit is 3.9 x 10⁴ light-years (1 light-year = 9.5 x 10¹⁵ m), and the angular speed of the star is 2.3 x 10^-15 rad/s. (a) Determine the tangential speed of the star. (b) What is the magnitude of the net force that acts on the star to keep it moving around the center of the galaxy?

Expert Solution

genius_generous answered 7 months ago

A string of length L = 1 is held fixed at both ends. The string is...

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