Circular Motion

A car of mass $m$ is driving over an arched bridge. The top of the bridge can be approximated as a circular arc with radius $R$.

As shown in Figure, a motorcycle is turning on a slope with an inclination angle of $\alpha$. The coefficient of static friction between the motorcycle and the slope is $\mu$. The radius of the circular track is $R$.

A police officer of mass $m$ drives her car through a circular turn of radius $R$ with a constant speed $v$.

A person of mass $m$ rides a Ferris wheel in a vertical circle of radius $R$ at a constant speed $v$.

A roller-coaster car of mass $m$ passes over the top of a circular hill of radius $R$. Assume its speed is not changing.

One end of a string is fixed, and a heavy ball is attached to the other end, forming a conical pendulum. The ball rotates in a horizontal plane. The string has a length of $L = 0.28$ m. When the pendulum rotates with a period of $P = 1.00$ s, the string makes an angle of $\theta = 30^\circ$ with the vertical.

A car is driven at a constant speed $v$ over a circular hill and then into a circular valley, both with the same radius $R$. The driver has a mass $m$. At the top of the hill, the normal force on the driver from the car seat is zero.

A car with a mass of 100 kg is traveling on a horizontal curved road with a radius of 300 m. The coefficient of static friction between the car and the road surface is 0.3.

A passenger of mass $m$ is in uniform circular motion along a path of radius $r$. The magnitude of the net centripetal force is $F$.

The gauge of a railway is 1435 mm. The radius of a circular arc at a railway turn is 300 m, and the specified speed for a train passing through this section is 20 m/s.