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Circular Motion

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?

Mechanics: Motion on incline, Banking ot tracks, Projectile.

Please see the attached spreadsheet. Thank you so much. These are not jokes but are problems from a teacher wishing to have a little fun with his students.

Motion in Vertical 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

Motion of a particle on a circle.

A particle undergoes uniform circular motion of radius 26.1 &#956;m 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?

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?

Simple Harmonic Motion in an Oscillator

The position of a simple harmonic oscillator is given by x(t)=(0.5m)cos((pi/3)t) where t is in seconds. What is the maximum velocity of this oscillator?

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

Vertical Circular Motion Problem

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?

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

Banking angle of velodrome.

A velodrome is built for use in the Olympics. The radius of curvature of the surface is 20 m. At what angle should the surface be banked for cyclists moving at 18m/s? (choose an angle so that no frictional force is needed to keep the cyclists in their circular path. Large banking angles are used in velodromes.)

Car Circular Motion

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

geodesic on the surface of a right circular cylinder

See attached file for full problem description. Show that the geodesic on the surface of a right circular cylinder is a segment of a helix. Notes: when it syas "show" the path, use the techniques oof calculus of variations to find an equation y = f(x), z = f(x,y) for the path, then explain how this function is the type of

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: Locked Brakes

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

Time taken by the wave on a stretched string.

A 15.0 kg ball is being whirled in a circular path on the end of a string. The motion occurs on a frictionless, horizontal table. The angular speed of the ball is w= 12.0 rad/s. The string has a mass of 0.0230 kg. How much time does it take for a wave on the string to travel from the center of the circle to the ball?

Helical Wire : Mass, Center of Mass and Moment of Inertia

Consider a wire in the shape of a helix with constant density function . A. Determine the mass of the wire: B. Determine the coordinates of the center of mass: ( , , ) C. Determine the moment of inertia about the z-axis: Note: If a wire with linear density lies along a space curve , its moment of inertia about th

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

Centripetal force for a road bank

At what angle should a curve of radius 150 m be banked, so that cars can travel safely at 25 m/s without relying on friction?

In a skating stunt known as the "crack the whip"

In a skating stunt known as the "crack the whip", a number of skaters hold hands and form a straight line. They try to skate so that the line rotates about the skater at one end, who acts as the pivot. The skater farthest out has a mass of 80.0 kg and is 6.10 m from the pivot. He is skating at a speed of 6.80 m/s. What is the ma

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.

Wave motion and equation of waves.

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