8. Centripetal Forces & Gravitation

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.

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 velocity.

As the earth rotates, what is the speed of a physics student in Miami, Florida, at latitude 26°. Ignore the revolution of the earth around the sun. The radius of the earth is 6400 km.

The earth's radius is about 4000 miles. Kampala, the capital of Uganda, and Singapore are both nearly on the equator. The distance between them is 5000 miles. The flight from Kampala to Singapore takes 9.0 hours. What is the plane's angular velocity with respect to the earth's surface? Give your answer in °/h.

Peregrine falcons are known for their maneuvering ability. In a tight circular turn, a falcon can attain a centripetal acceleration 1.5 times the free-fall acceleration. What is the radius of the turn if the falcon is flying at 25 m/s?

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?

A bug walks outward from the center of a turntable that is rotating at 65 rpm. If the coefficient of static friction between the bug and the turntable is 0.42, how far out from the center does the bug get before it starts to slip on the turntable? What happens to the bug after it moves farther out past that point?

A coin is placed 10.5 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 38.0 rpm (revolutions per minute) is reached, at which point the coin slides off. What is the coefficient of static friction between the coin and the turntable?

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?

FIGURE P8.54 shows two small 1.0 kg masses connected by massless but rigid 1.0-m-long rods. What is the tension in the rod that connects to the pivot if the masses rotate at 30 rpm in a horizontal circle?

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.

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 tension in the string?

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.

The position of a particle moving in the xy plane is given by $\vec{r}=\left(2.0\text{m}\right)\cos \left[\left(3.0\frac{\text{rad}}{\text{s}}\right)t\right]\hat{i}+\left(2.0\text{m}\right)\sin \left[\left(3.0\frac{\text{rad}}{\text{s}}\right)t\right]\hat{j}$, where r is in meters and t is in seconds. Show that the acceleration vector always points toward the center of the circle.

How many revolutions per minute would a 22-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost point?