8. Centripetal Forces & Gravitation

A ball travels on a frictionless circular track at 3m/s. The ball cannot have an acceleration greater than 1.5m/s² or it will go off the track. What is the smallest radius the circular track can have so that the ball stays on the track?

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 train traveling at a constant speed rounds a curve of radius 215 m. A lamp suspended from the ceiling swings out to an angle of 18.5° throughout the curve. What is the speed of the train? [Hint: See Example 4–15.]

In uniform circular motion, a ball of mass $m$ moves in a vertical loop of radius $R$. What is the maximum possible speed of the ball at the top of the loop such that it just maintains contact with the track?

In which of the following situations would a space probe most likely experience $centripetalacceleration$?

Which of the following situations during a basketball game involves $\mathrm{centripetal} \mathrm{acceleration}$?

$$In a uniform circular motion, which of the following statements about the direction of acceleration is correct?

A uniform thin rod of mass $m$ and length $L$ is rotating with constant angular speed $\omega$ about an axis perpendicular to the rod and passing through one end. What is the magnitude of the centripetal force acting on the rod as it rotates?

A uniform wire with mass $m$ and length $l$ is bent into a semicircle. What is the magnitude of the moment of inertia of the wire about an axis passing through the center of the semicircle and perpendicular to its plane?

An alpha particle with charge $q$ and mass $m$ moves at constant speed $v$ in a uniform magnetic field of magnitude $B$, perpendicular to its velocity. What is the radius of its circular path?

As a car goes through a turn on a level road, what provides the necessary $centripetal$ force to keep the car moving in a circular path?

In uniform circular motion, in which direction must the net force always act on the particle?

An astronaut is being tested in a centrifuge that rotates at constant speed in a horizontal circle of radius $r$. If the astronaut's mass is $m$ and the speed of rotation is $v$, what is the magnitude of the net force acting on the astronaut toward the center of the circle?

In the context of $\mathrm{uniform} \mathrm{circular} \mathrm{motion}$, what is the shape of the trajectory that a $\mathrm{charged} \mathrm{particle}$ follows when moving $\mathrm{perpendicular}$ to a $\mathrm{uniform} \mathrm{magnetic} \mathrm{field}$?

In uniform circular motion, which statement correctly describes the $\mathrm{speed}$ and $\mathrm{velocity}$ of an object moving in a circle at constant $\mathrm{speed}$?