Couple of problems Please help

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In summary, the conversation discusses various scenarios involving angular speed, tangential speed, and centripetal acceleration. In the first scenario, a baton twirler throws a baton directly upward and it completes 4.42 revolutions before returning to the twirler's hand. If the angular speed of the baton is 1.95 rev/s, the height to which the center of the baton reaches can be determined by using the equation h = (1/2) * (w^2) * (r), where h is height, w is angular speed, and r is radius.Next, the conversation discusses a planet orbiting a star in a nearly circular orbit with a radius of 1.56 x
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1)A baton twirler throws a spinning baton directly upward. As it goes up and returns to the twirler's hand, the baton turns through 4.42 revolutions. Ignoring air resistance and assuming that the average angular speed of the baton is 1.95 rev/s, determine the height to which the center of the baton travels above the point of release.


2)A planet orbits a star, in a year of length 4.57 x 107 s, in a nearly circular orbit of radius 1.56 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 and direction of the planet's centripetal acceleration.

3)A rectangular plate is rotating with a constant angular speed about an axis that passes perpendicularly through one corner, as the drawing shows. The centripetal acceleration measured at corner A is n times as great as that measured at corner B. What is the ratio L1/L2 of the lengths of the sides of the rectangle when n = 1.66?

4)A star has a mass of 1.81 x 1030 kg and is moving in a circular orbit about the center of its galaxy. The radius of the orbit is 3.1 x 104 light-years (1 light-year = 9.5 x 1015 m), and the angular speed of the star is 2.5 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?

All help is appreciated, thank you
 
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Hi jellis26, welcome to PF.
Go through the textbook. Collect the relevant equations to solve the problem.
show your attempts.
 

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