8. Centripetal Forces & Gravitation

A jet plane traveling 1890 km/h (525 m/s) pulls out of a dive by moving in an arc of radius 4.80 km. What is the plane's acceleration in g's?

In a system where mass $m_1$ rotates in a horizontal circle of radius $r$ on a frictionless table, attached by a string passing through a hole to a hanging mass $m_2$ (which remains at rest), what must be the speed of $m_1$ for $m_2$ to stay stationary?

The radius of the earth's very nearly circular orbit around the sun is 1.5 x 10¹¹ m. Find the magnitude of the earth's angular velocity.

A 200 g block on a 50-cm-long string swings in a circle on a horizontal, frictionless table at 75 rpm. What is the speed of the block?

In uniform circular motion, how long does it take the bob to make one full revolution (one complete trip around the circle)?

If a car traveling in a circular path suddenly encounters ice and friction becomes negligible, what will happen to the car's motion?

In uniform circular motion, how do $\mathrm{inertia}$ and $\mathrm{centripetal} \mathrm{force}$ interact to keep an object moving in a circle?

The earth has a radius of 6380 km and turns around once on its axis in 24 h. What is the radial acceleration of an object at the earth's equator? Give your answer in m/s² and as a fraction of g.

For a wheel rolling to the right without slipping, what is the direction of the velocity of the point at the very top of the wheel relative to the ground?

Suppose the moon were held in its orbit not by gravity but by a massless cable attached to the center of the earth. What would be the tension in the cable? Use the table of astronomical data inside the back cover of the book.

The position of a particle moving in the xy plane is given by $\overrightarrow{r}$ = (2.0m) cos [(3.0 rad/s)t ] $\hat{i}$ +(2.0m) sin [(3.0 rad/s)t ] $\hat{j}$, where r is in meters and t is in seconds. Calculate the velocity and acceleration vectors as functions of time.

In uniform circular motion, what is the name of the force that acts toward the center of the circle to overcome inertia and keep an object moving along a curved path?

In a “Rotor-ride” at a carnival, people rotate in a vertical cylindrically walled “room.” See Fig. 5–52. If the room radius is 5.5 m, and the rotation frequency 0.50 revolutions per second when the floor drops out, what minimum coefficient of static friction keeps the people from slipping down? People on this ride said they were “pressed against the wall.” Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides nausea)? [Hint: Draw a free-body diagram for a person.]

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In the context of uniform circular motion, what is the best description of the $\mathrm{centrifugal force;}$ as discussed in drivers education classes?