How many revolutions per minute would a $15$-m-diameter Ferris wheel need to make for the passengers to feel "weightless" at the topmost point of the trip?

At what minimum speed must a roller coaster be traveling when upside down at the top of a circle so that the passengers will not fall out? Assume a radius of curvature of 7.4 m.

A coin is placed 11.0 cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?

What is the maximum speed with which a $1050$-kg car can round a turn of radius $70$ m on a flat road if the coefficient of friction between tires and road is $0.80?$ Is this result independent of the mass of the car?

A sports car crosses the bottom of a valley with a radius of curvature equal to $95 \mathrm{~m}$. At the very bottom, the normal force on the driver is twice his weight. At what speed was the car traveling?

Six artificial satellites complete one circular orbit around a space station in the same amount of time. Each satellite has mass m and a radius of orbit L. The satellites fire rockets that provide the force needed to maintain a circular orbit around the space station. The gravitational force is negligible.Rank the net force acting on each satellite from their rockets.

Rank from largest to smallest. To rank items as equivalent, overlap them

A) m = 200 kg and L = 5000 m

B) m = 400 kg and L = 2500 m

C) m = 100 kg and L = 2500 m

D) m = 100 kg and L = 10000 m

E) m = 800 kg and L = 5000 m

F) m = 300 kg and L = 7500 m

You travel to another planet in our solar system and find that your weight is twice as large as it is on Earth. If the radius of this planet is twice the Earth's radius, is the mass of the planet (a) two times the Earth's mass, (b) four times the Earth's mass, (c) half of the Earth's mass, or (d) eight times the Earth's mass?

A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm's length) of radius 0.90 m. Calculate the speed of the discus.

Calculate the speed of a satellite moving in a stable circular orbit about the Earth at a height of $4800 \mathrm{~km}$.

A jet plane traveling 1890 km/h (525 m/s) pulls out of a dive by moving in an arc of radius 6.00 km. What is the plane's acceleration in g's?

What is the maximum speed with which a $1200$ kg car can round a turn of radius $75$ m on a flat road if the coefficient of static friction between tires and road is $0.80$? Is this result independent of the mass of the car?

How fast (in rpm) must a centrifuge rotate if a particle $7.0$ cm from the axis of rotation is to experience an acceleration of $100,000 ~g$'s$?$

A certain neutron star has five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monster.

Every few hundred years most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line. The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, M_{\mathrm{S}}=95.1 M_{\mathrm{E}},$ and their mean distances from the Sun are 108, 150, 778, and 1430 million km, respectively. What fraction of the Sun's force on the Earth is this?