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# Circular Motion

Circular motion is the movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform or non-uniform with the rate of rotation. Due to the object’s constantly changing direction of the velocity vector, the object undergoes acceleration by a centripetal force. Without the acceleration, the object would move in a straight line according to Newton’s laws of motion.

Velocity is tangent to the circular path. No two velocities point in the same direction. The object may have constant speed, but the direction is always changing. For a path of radius r, and where the angular rate of rotation is ω, velocity is defined as:

v= rω

Thus velocity is constant at the same angular rate of rotation. Acceleration of circular motion is defined as:

a= v^2/r

Non-uniform circular motion is where the object is moving in a circular path has a varying speed. The tangential acceleration is non-zero however, the speed is changing. Due to the non-zero tangential acceleration, there are forces that act on an object in addition to the centripetal force. These forces can include weight, normal force and friction.

## BrainMass Categories within Circular Motion

### Rate of deceleration

An automobile traveling 68 MPH strikes a bridge abutment. Due to crumpling of the front of the car, its occupants undergo 29 inches of constant deceleration distance. Estimate the rate of deceleration, in ft/s2, that the occupants of the car will experience. State your answer rounded to the nearest ft/s2. (Note: 60 MPH = 88 ft/s

### Expanding & Contracting Sphere Harmonic Motion Model

I am trying to model the harmonic motion of an expanding and contracting sphere. In this case, the origin of the spherical oscillation is not a point source but rather a sphere with a time varying radius. i.e the volume of the sphere is expanding and contracting to a non point source.

### Circular Motion

What angle of bank is necessary for a car to make it around a 130m curve at a speed of 60kph without relying on friction?

### Pendulum and Peg

A point mass on a mass-less string of length L is supported as a pendulum. A peg of negligible radius is placed a distance d directly below the support point. The mass is released from a horizontal position (theta = 90 degrees). Find the minimum value of d (in terms of L) such that the mass will make a complete circle around

### Magnetic Field Sample Solution

An electron, mass 9.11 * 10^-31 kg, moves at 9.2 * 10^6 m/s in a uniform magnetic field of .0054 Tesla, with the field perpendicular to the velocity of the electron. What will be the radius of the circular path of the electron? If the field is directed downward and the electron moves to the North, will it circle in a clockwis

### Centripetal force explained in this solution

A car moving at 25 m/s drives over the top of a hill. The top of the hill forms an arc of a vertical circle 121 meters in diameter. i) What is the centripetal force holding the car in the circle? ii) What, therefore, is the normal force between the car's tires and the road?

### Magnetic Fields: Motion Moves in a Circle

A charged particle travel ling to the right (assume in the plane of the paper) is injected into an area in which the magnetic field is directed out toward you. What will be the resulting motion of the particle? How much work will the magnetic field do on the charged particle as a result? Explain. Does the motion move in a cir

### Three Charged Particles Injected into a Uniform Magnetic Field

See attached file for diagram. Please solve and explain. Three charged particles are injected into a uniform magnetic field -- all of the particles have the same speed, but their masses and charges are different. Which of the following statements are true? 1. (T/F) Particle #2 is negatively charged 2. (T/F) If they

### Harmonic Motion: 8 Questions

See attached file.

### Basic principles of harmonic motion

A spring with a force constant of 35 N/m is attached to a 0.59 kg mass. Assuming that the amplitude of motion is 3.1 cm, determine the following quantities for this system. (a) &#969; ______s-1 (b) vmax ______m/s (c) T ______s

### Centripetal Force.

A model airplane of mass 0.830 kg flies in a horizontal circle at the end of a 54.0 m control wire, with a speed of 35.0 m/s. Compute the tension in the wire if it makes a constant angle of 20.0° with the horizontal. The forces exerted on the airplane are the pull of the control wire, the gravitational force, and aerodynamic li

### Magnetic Field: Motion of a charged particle

Please help with the following physics problem. Provide step by step calculations. Describe the path of an electron that is projected vertically upward with a speed of 2.30 106 m/s into a uniform magnetic field of 0.190 T that is directed away from the observer. The electron will travel in a (clockwise vertical, clockwise

### The Period of Oscillations

An ice cube can slide around the inside of a vertical circular hoop of radius R. It undergoes small-amplitude oscillations if displaced slightly from the equilibrium position at the lowest point. Find an expression for the period of these small-amplitude oscillations. Give your answer in terms of R and constants g and pi.

### Physics - Mechanics - Circular Motion Problems

The tub of a washer goes into its spin-dry cycle, starting from rest and reaching an angular speed of 5.0 rev/s in 8.0 s. At this point, the person doing the laundry opens the lid and safely switch turns off the washer. The tub slows to rest in 12.0 s. Through how many revolutions does the tub turn during the entire 20-s interva

### Circular Motion

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 a.) velocity b.) angular veloctiy and c.) centripetal acceleration as it travels around the sun. Assume a year of 365 days.

### Equations of motion in a rotatin frame

A student is performing measurements with a hockey puck on a large merry-go-round with a frictionless, horizontal, flat surface end has a constant angular velocity of W(bar) and rotates counter clockwise as seen from above. Given: the radius of the merry-go-round is R= 1m, W(bar)=1 radian/sec. Initial position is: x=-.5R

### Direction of a Moving Particle in a Charged Particle

1) The neutron is a particle with zero charge. However, it has a nonzero magnetic moment of 9.66 × 10−27Am2. A possible explanation for this is the circular motion of 'quarks' - fundamental subatomic particles. The neutron is believed to consist of an "up" quark with a charge of +2e/3 and two "down" quarks each of charge −e

### A bead slides down a circular loop made of wire. To determine its speed and normal reaction on it.

A bead slides on a smooth rigid wire bent into the form of a circular loop of radius b. If the plane of the loop is vertical and if the bead starts from rest at a point that is level with the center of the loop, find the speed of the bead at the bottom and the reaction of the wire on the bead at that point.

### tension on a string

A ball on the end of a string is cleverly revolved at a uniform rate in a vertical circle of radius 75.0 cm, as shown in Fig. 5-33. Its speed is 4.10 m/s and its mass is 0.300 kg. Figure 5-33. (a) Calculate the tension in the string when the ball is at the top of its path. N (b) Calculate the tension in the string when

### Mechanics: Motion on Curved Banked Track with Friction

A 1700 kg car rounds a curve of radius 70 m banked at an angle of 12°. If the car is traveling at 80 km/h, will a friction force be required? If so, how much force? (Enter zero if there is no friction force).

### car passes through a bump

Please see the attached file. A car of mass m passes over a bump in a road that follows the arc of a circle of radius R, as in the figure below. (a) What force does the road exert on the car as the car passes the highest point of the bump if the car travels at a speed v? (Use m, g, v, and R as necessary.) (b) What is the

### oscillation equation as a function of time

Please see the attached file. A weight of mass m is hung from the end of a spring which provides a restoring force equal to k times its extension. The weight is released from rest with the spring unextended. Find its position as a function of time, assuming negligible damping.

### Circular Motion; Banking of Highway Curves

1. Highway curves are usually banked at an angle theta such that the horizontal component of the reaction force of the road on the car traveling at the design velocity equals the required centripetal force. Find the proper banking angle for a car making a turn of radius r at velocity v. Please see the force diagram in the at

### 2 Problems on Motion on circular Path: Centripetal force

1. A 1000 kg car rounds a turn of radius 30m at a velocity of 9 m/s. (a) How much centripetal force is required? (b) Where does this force come from? 2. The maximum force a road can exert on the tires of a 3200 lb car is 2000 lb. What is the maximum velocity at which the car can round a turn of radius 320 ft?

### The device consists of two rotating discs, separated by a given distance and rotating with a given angular speed. The bullet first passes through the left disc and then through the right disc. Angular displacement between the two bullet holes is given. Determine the speed of the bullet.

The drawing (see attachment) shows a device that can be used to measure the speed of a bullet. The device consists of two rotating discs, separated by a distance d = 0.85m and rotating with an angular speed of 95 rad/sec. The bullet first passes through the left disc and then through the right disc. It is found that the angular

### Rigid Body Dynamics Problems

Please do probs 6/148 and 6/136 only. Refer attachment for fig. Problem 6/148 : The fig. shows cross section of a garage door which is a uniform rectangular panel 8 x 8 ft ans weighing 200 lb. The door carries two spring assemblies, one on each side of the door, like the one shown. Each spring has a stiffness of 50 lb/ft, and

### Rigid Body Dynamics Problems

Problem 1 : To determine moment of inertia about different axes of rotation of a circular disc of given radius of gyration. Problem 2 : A two pulley system. To determine acceleration, tension in the cable etc.

### Distance Traversed by Particle on Surface of Rotating Disk

A spinning disk (i.e., a rotating disk) has a radius of 6 cm (6 centimeters) and a constant rate of rotation of 7200 rpm (7200 revolutions per minute). Find the total distance traversed in 5 seconds by a particle of dust that lies at a point on the surface of the disk which is at a distance of 2.5 cm from the center. Express you

### Rotational Dynamics - Angular Acceleration

Link OA has a constant counterclockwise angular velocity w during a short interval of its motion. For the position shown determine the angular accelerations of AB and BC. Please see the attached document for the diagram.

### the centripetal force the fly without slippling

A fly mass 0.300 grams is sunning itself on a phonographic turntable at a distance of 6 cm from the center. The turntable is turned on and rotates 45 rpm. Whats the centripetal force the fly needs to exert to avoid slipping?