Spacecraft orbiting -- need to find the period

A spacecraft is in orbit around Jupiter. The radius of the orbit is 3.0 times the radius of Jupiter (RJupiter = 71,500 km). The gravitational acceleration at the surface of Jupiter (the surface is defined as the above radius) is 23 m/s2. Without using any other information about Jupiter, what is the period of the spacecraft's orbit? Please solve this numerically with the numbers I have provided to find the answer. Please show all work too. Thanks.

Block Sliding down a frictionless plane at an angle

A 4.0 kg block is released from rest at the top of a frictionless plane of length 8.0 m that is inclined at an angle of 15° to the horizontal. A cord is attached to the block and trails along behind (assume the cord is massless). When the block reaches a point 5.0 m along the incline from the top, someone grasps the cord and exerts a constant tension parallel to the incline. The tension is such that the block just comes to rest when it reaches the bottom of the incline. (The person's force is nonconservative!) What is this constant tension? Solve the problem twice, once using work and energy and again using Newton's laws and constant acceleration kinematics. Please solve numerically ... click for more

Rotation problems

1. At t=0, a fly wheel has an angular velocity of 4.7 rad/s (radians per second), an angular acceleration of -0.25 rad/s^2 , and a reference line at pheta0 = 0. (a) Through what maximum angle phetamax will the reference line turn in the positive direction ? At what times t will the reference line be at (b) pheta = 1/2phetamax and (c) pheta = -10.5 rad (consider both positive and negative values of t ) ? 2. (a) What is the angular speed w about the polar axis of a point on Earths surface at a latitude of 40 degrees N ? ( earth rotates about that axis ) (b) What is the linear speed v of the point ? What are (c) w and (d) v for a point at the equator ? 3. A record turntable is rotating ... click for more

Find Kinetic energy of earth due to its rotation about its axis.

Assume the Earth is a uniform solid sphere. Find the kinetic energy of the Earth due to its rotation about its axis. Suppose we could somehow extract 1.0% of the Earth's rotational kinetic energy to use for human needs. By how much would that change the length of the day? For how many years would 1.0% of the Earth's rotational kinetic energy supply the world's energy needs, assuming these needs are a constant 1.0 ´ 1021 J per year? Please solve numerically and show all work. Thanks.

Ball rolling down in incline, then through a loop to loop -- find speed neccesary to complete the loop.

A solid steel ball of radius r rolls down an incline into a loop-the-loop of radius R. What is the minimum speed the ball must have at the top of the loop in order to stay on the track? At what vertical height on the incline, in terms of the radius of the loop, must the ball be released in order for it to have the required minimum speed at the top of the loop, neglecting any frictional losses?