mass m rotates at constant speed v at a radius of R from the rotational exis. A force F provides centripetal force Fc . If you double both, the mass m and the radius R of the motion,without v, the force needed to keep the mass in circular motion would (a) stay the same (b) double (c) halve (d) quadruple

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.

Zorch, an archenemy of Superman, decides to slow Earth's rotation to once per 29.5 h by exerting a force parallel to the equator, opposing the rotation. Superman is not immediately concerned, because he knows Zorch can only exert a force of 3.95 x 107 N. For the purposes calculations in this problem you should treat the Earth as a sphere of uniform density even though it isn't. Additionally, use 5.979 x 1024 kg for Earth's mass and 6.376 x 106 m for Earth's radius. How long, in seconds, must Zorch push with this force to accomplish his goal? (This period gives Superman time to devote to other villains.)

A 5 kg mass is spun around in a circle of radius 2m with a period of 7 s. What equation would you use to find the centripetal force acting on the mass? Calculate the centripetal force acting on the mass. Possible Formulas that can be used to answer the question: v=(2πr)/T ac=v2/r ac=(4π2r)/T2 Fc=mac Fg=mg F=(Gm1m2)/d2 g=Gm/r2 T2=(4π2/Gm)r3 v=√(Gm)/r g=9.80m/s2 G=6.67x10-11 (N∙m2)/kg2