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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: 144

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

Rotation

Postings: 197

A rotation is circular movement around an objects center.

Torques

Postings: 240

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

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

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

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

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.

Rotational motion of a skater.

A 52 kg ice skater spins about a vertical axis through her body with her arms horizontally outstretched, making 2.0 turns each second. The distance from one hand to the other is 1.50m. Biometric measurements indicate that each hand typically makes up about 1.25% of body weight. What horizontal force must her wrist exert on her

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

sideways force on the train passenger

Consider a train that rounds an unbanked curve with a radius of 600m at a speed of 160 km/hr. The sideways force on a train passenger of 70 kg is equal to?

Motion in verticle circle: Force and tension.

A piece of stone m=5kg is attached to a string with length r=80 cm and is rotating in a VERTICAL circular path with constant speed of v=10m/s a) draw a figure, show forces acting on the stone when it is on the highest and lowest positions. (Don't forget the gravity) b) draw a free body diagram for each of the two situations

Physics

A wheel starts from rest and has an angular acceleration of 4.0 rad/s^2. How long does it take for the wheel to complete 10 full revolutions?

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

Vertical Circular Motion

Suppose the surface (radius = r) of the space station in Figure 5.19 is rotating at 33.8 m/s. What must be the value of r for the astronauts to weigh one-half of their earth weight?

Circular Motion

A car crests a hill at an extreme velocity and "gets air". Explain the physics of why this is.

Equation of Motion and other Physics Problems

6 What is the equation of motion for the idealized model shown? 7 For the idealized system shown, what is the natural circular frequency in rad/sec, and the period of oscillation in seconds? 1 The equivalent spring constant of two parallel springs with spring constants 20 lb/in., and 50 lb/in. is: 8 A Mass-Spring-Damp

Circular Motion

Why is it necessary to never allow brakes to lock up in order to successfully pull out of a skid on the ice?

A block suspended above the ground by a light rope wrapped around a pulley wheel, is released allowing it to rotate freely, letting the block fall to the ground. To determine the rotational speed, speed, time to reach the ground.

A 2 Kg block is suspended 5 m above the ground by a light rope wrapped around a 3 kg solid pulley wheel, as shown in figure. The pulley wheel, which was initially at rest, is then released allowing it to rotate freely, letting the block fall to the ground. Ignoring friction effects the rope mass: (a) Briefly state where, a

Physics of Ski Jump

A skier starts from rest at the top of a hill. The skier coasts down the hill and up a second hill, as the drawing (attached) illustrates. The crest of the second hill is circular, with a radius of r=36 m. Neglect friction and air resistance. What must be the height H of the first hill so that the skier just loses contract with

Motion and Wedge Reaction

A particle of mass m slides down a smooth circular wedge (radius = R) of mass M (see fig). The wedge rests on a smooth horizontal table. a) Find the equation of motion of m and M b) The reaction of the wedge on m See attached file for full problem description.

Lagrangian Dynamics.

A circle of radius R, oriented with the plane of the circle horizontal, is attached to a vertical axis at one point on the circumference of the circle. A bead, of mass m, is attached to the circle and is free to move around the circle, with no frictional losses. The circle - bead system rotates about the axis at a constant

Magnetic fields- Solar wind

The solar wind is a thin, hot gas given off by the sun. Charged particles in this gas enter the magnetic field of the earth and can experience a magnetic force. Suppose a charged particle traveling with a speed of 9.0 X 10^6 m/s encounters the earth's magnetic field at an altitude where the field has a magnitude of 1.2 X 10^-7T.

A plane progressive harmonic wave

A plane progressive harmonic wave is represented by the equation (see attached) where is the displacement in meters, t is the time in seconds and x is distance from a fixed origin in meters. Determine the following wave properties, and where appropriate give units: a) The amplitude b) The direction of wave travel c) Th

What Is and Is Not Torsion

One definition of torsion is the act of twisting or turning. Would this apply to the following examples? - helicopter blades normally rotating around - knees and arms bending

Simple harmonic motion

Please see the attached files for full description. 15. The displacement of a mass oscillating on a spring is given by x(t) = x_m * cos(wt + ph). If the initial displacement is zero and the initial velocity is in negative x direction, then the phase constant phi is: 16. Mass m, oscillating on the end of a spring with sprin

Rotational or Angular Simple Harmonic Motion

Your boss at the Cut-Rate Cuckoo Clock Company asks you what would happen to the frequency of the angular SHM of the balance wheel if it had the same density and the same coil spring (thus the same torsion constant), but all the balance wheel dimensions were made one-third as great to save material. 1) By what factor would th

Motion on a vertical circle.

This problem is a three-parter. Here we go: A stunt man whose mass is 72.7 kg swings from the end of a 4.51 m long rope along the arc of a vertical circle. 1.) Assuming he starts from rest when the rope is horizontal, find the tension in the rope that is required to make him follow his circular path at the beginning of hi