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28 problems tagged with Circular Motion in Dynamics
P0348
Intermediate Mechanics › DynamicsMaximum Speed on a Banked Frictional Turn
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 $R$.
P0427
Beginner Mechanics › DynamicsNet Force on Officer in Circular Turn
A police officer of mass $m$ drives her car through a circular turn of radius $R$ with a constant speed $v$.
- What is the magnitude of the net force of the officer on the car seat?
- What is the angle of this force relative to the vertical?
P0428
Beginner Mechanics › DynamicsForces on a Ferris Wheel Rider
A person of mass $m$ rides a Ferris wheel in a vertical circle of radius $R$ at a constant speed $v$.
- What is the period of the motion?
- What is the magnitude of the normal force on the person from the seat at the highest point?
- What is the magnitude of the normal force on the person from the seat at the lowest point?
P0429
Beginner Mechanics › DynamicsRoller Coaster on a Circular Hill
A roller-coaster car of mass $m$ passes over the top of a circular hill of radius $R$. Assume its speed is not changing.
- What is the magnitude and direction of the normal force $F_N$ on the car from the track if the car's speed is $v_1$, where $v_1 < \sqrt{gR}$?
- What is the magnitude and direction of the normal force $F_N$ on the car from the track if the car's speed is $v_2$, where $v_2 > \sqrt{gR}$?
P0363
Beginner Mechanics › DynamicsCalculating Gravity with a Conical Pendulum
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.
P0430
Beginner Mechanics › DynamicsNormal Force on Driver in Hill and Valley
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.
P0366
Beginner Mechanics › DynamicsMaximum Speed of a Car on a Curved Road
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.
P0431
Beginner Mechanics › DynamicsCentripetal Force vs. Speed and Period
A passenger of mass $m$ is in uniform circular motion along a path of radius $r$. The magnitude of the net centripetal force is $F$.
- A plot of $F$ versus the passenger's speed $v$ is generated as in Figure a. What is the plot's slope at a given speed $v$?
- A plot of $F$ versus the period of motion $T$ is generated as in Figure b. What is the plot's slope at a given period $T$?
P0369
Beginner Mechanics › DynamicsBanked Railway Curve for a Train
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.
P0425
Beginner Mechanics › DynamicsForce on an Arched Bridge by a Car
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 $R$.
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