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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.

Categories within Circular Motion

Orbits

Postings: 143

An orbit rotates gravitationally around a fixed point at an equal distance.

Rotation

Postings: 195

A rotation is circular movement around an objects center.

Torques

Postings: 238

Torque is the tendency of an object to rotate around an axis.

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

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) ω ______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

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

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.

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.

the moment of inertia of the stool

A solid circular disk has a mass of 1.2 kg and a radius of 0.16m. Each of three identical thin rods has a mass of 0.15 kg. The rods are attached perpendicularly to the plane of the disk at its outer edges to form a three legged stool (simple drawing of a three legged stool provided). Find the moment of inertia of the stool wi

Motion of a particle on a circle.

A particle undergoes uniform circular motion of radius 26.1 μm in a uniform magnetic field. The magnetic force on the particle has a magnitude of 1.60 x 10-17 N. What is the kinetic energy of the particle?

average angular acceleration of the CD

A certain CD has a playing time of 78 minutes. When the music starts, the CD is rotating at an angular speed of 4.8 * 10^2 revolutions per minute (rpm). At the end of the music, the CD is rotating at 2.1 * 10^2 rpm. Find the magnitude of the average angular acceleration of the CD. Express your answer in rad/s2.

Rotational Kinematics and Projectile Motion.

At the local swimming hole, a favorite trick is to run horizontally off a cliff that is 8.9 m above the water. One diver runs off the edge of the cliff, tucks into a "ball," and rotates on the way down with an average angular speed of 1.2 rev/s. Ignore air resistance and determine the number of revolutions she makes while on the

Centripetal Force

A block is hung by a string from the inside roof of a van. When the van goes straight ahead at a speed of 33 m/s, the block hangs vertically down. But when the van maintains this same speed around an unbanked curve (radius = 140 m), the block swings toward the outside of the curve. Then the string makes an angle with the vertica