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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: 145

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

Rotation

Postings: 200

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

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

Two problems on rigid body dynamics

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.

Centripetal force

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?

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