Consider a non-rotating space station in the shape of a long thin uniform rod of mass 2.94 x 10^6 kg and length 1075 meters. Rocket motors on both ends of the rod are ignited, applying a constant force of F = 8.56 x 10^5 N to each end of the rod as shown in the diagram, causing the station to rotate about its center. If the motors are left running for 2 minutes and 29 seconds before shutting off, then how fast will

One end of a cord is fixed and a small 0.400-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 1.50 m, as shown in the figure below. When θ = 23.0°, the speed of the object is 5.50 m/s. An object is swinging to the right and upward from the end of a cord attached to a horizontal surface. The cord makes an angle θ with the vertical. An arrow labeled vector v points in the direction of motion. (a) At this instant, find the magnitude of the tension in the string.Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. N(b) At this instant, find the tangential and radial components of acceleration. at = Your response differs from the correct answer by more than 100%. m/s2 downward tangent to the circle ac = Your response differs from the correct answer by more…

Suppose that humans have created a colony outside of our solar system on a planet called Wfirst21. Wfirst21 has a mass of 2.65×1025 kg2.65×1025 kg and a day that lasts 23.7 h23.7 h (which defines the rotational period of the planet). The colony is located on the planet's equator. The colonists set up a communications satellite which orbits Wfirst21. The satellite has a circular orbit that keeps it positioned directly above the colony. Calculate the radius ?r of the satellite's orbit in kilometers.

A tetherball is connected to the top of a pole with a rope that is 2.58m long and swings around the pole at an angle of θ = 33.4 degrees between the pole and the rope. Calculate the speed of the tetherball in meters/second, but only enter in the numerical value, do NOT enter units.

A large wind turbine (typical of the size and specifications of a turbine that you see in a modern wind farm) has three blades connected to a central hub. The blades are 50 m long and rotate at 10 rpm. What angular speed ω does this correspond to? What is the speed ν of the tip of a blade? What is the speed of a point 25 m from the hub?

Suppose that humans have created a colony outside of our solar system on a planet called Wfirst21. Wfirst21 has a mass of 1.45×1025 kg and a day that lasts 24.1 h (which defines the rotational period of the planet). The colony is located on the planet's equator. The colonists set up a communications satellite which orbits Wfirst21. The satellite has a circular orbit that keeps it positioned directly above the colony. Calculate the radius ?r of the satellite's orbit in kilometers.

Problem 24:  An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: θ(t) = a + bt2 – ct3 where a = 1.1 rad, b = 0.35 rad/s2 and c = 0.025 rad/s3. Randomized Variablesa = 1.1 radb = 0.35 rad/s2c = 0.025 rad/s3 Part (a)  Determine an equation for the angular speed of the ride as a function of time, ω(t). Write your answer using the symbols a, b, and c, instead of their numerical values.  Part (d)  Determine an equation for the angular acceleration of the ride as a function of time, α(t). Write your answer using the symbols a, b, and c, instead of their numerical values.

6. Consider a non-rotating space station in the shape of a long thin uniform rod of mass 6.73 x 10^6 kg and length 809 meters. Rocket motors on both ends of the rod are ignited, applying a constant force of F = 6.84 x 10^5 N to each end of the rod as shown in the diagram, causing the station to rotate about its center. If the motors are left running for 2 minutes and 47 seconds before shutting off, then how fast will the station be rotating when the engines stop?     2.40 rpm     0.96 rpm     3.36 rpm     5.38 rpm

Zorch, an archenemy of Superman, decides to slow the Earth's rotation to once per 30.5 h by exerting an opposing force at the equator and parallel to it. Superman is not immediately concerned, because he knows Zorch can only exert a force of 4.60 x 10' N (comparable to a Saturn V rocket's thrust). Assume the Earth's initial rotation is exactly once per 24.0 h to find how long Zorch must push with this force to accomplish his goal. (This gives Superman time to devote to other villains. The Earth's mass is 5.98 × 1024 kg and its radius is 6.38 x 106 m.) Additional Materials |Reading