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# Rotation

### Plane Mirror and Light Rays

I had some questions about mirrors, please provide supporting equations and information for these problems. - Does the mirror equation (p^-1 + d^-1 = 2R^-1 = f^1) apply to a plane mirror? What relationship between p and d does it imply? - Why is it when you stand in front of a mirror your left appears on your right and your

### The Magnitude and Direction of Centripetal Acceleration

What is the magnitude and direction of the centripetal acceleration due to the earth's rotation at a location near Kansas City at 38 degrees latitude? I believe the answer is 2.66x10^-2 m/s^2, towards the earth's rotation axis. I need to see all formulas involved.

### Multiple Choice Question son Velocity and Tension

A particle moves according to the equation x = 10t2, where x is in meters and t is in seconds. Find the average velocity for the time interval from 2.0 second to 3.0 second. 50 m/s 100 m/s 250 m/s 200 m/s A particle undergoes three consecutive displacements: d1 = (10i + 30j + 12k), d2 = (23

### Frequency and amplitude of emf in wire loop

A stiff wire bent into a semicircle of radius a=2.0 cm is rotated at constant angular speed 40 rev/s in a uniform 20 mT magnetic field. What are the (a) frequency and (b) amplitude of the emf induced in the loop?

### Moment of inertia - Parallel-Axis Theorem

To solve many problems about rotational motion, it is important to know the moment of inertia of each object involved. Calculating the moments of inertia of various objects, even highly symmetrical ones, may be a lengthy and tedious process. While it is important to be able to calculate moments of inertia from the definition, in

### Moment of Inertia of two particles located in the x-y plane.

In this problem, you will answer several questions that will help you better understand the moment of inertia, its properties, and its applicability. --------- Diagram ------------------------ 1. On which of the following does the moment of inertia of an object depend? A. linear speed B. linear acceleration C.

### 11 Problems on Electromagnetism : A Complete Study

Please review the attached conceptual physics questions. Instead of just the answers, I would also like full explanations. This is so I can learn the material. Please make sure you are accurate and clear. Thanks. Please See attached word document

### Rotating cylindrical axle

You are to design a rotating cylindrical axle to lift 800-N buckets of cement from the ground to a rooftop 78.0 m above the ground. The buckets will be attached to a hook on the free end of a cable that wraps around the rim of the axle; as the axle turns, the buckets will rise. 1. What should the diameter of the axle be in or

### The Rotation Matrix

The rotation matrix [R], associated with a positive (in a right-hand sense) rotation α ; about the z-axis is: cosα sinα 0 -sinα cosα 0 0 0 1 ? Derive the rotation Matrix [Q] relating (x, y, z) to a system (x', y', z') which is described by three consecutive Euler rotations about z, then y

### Relativity : Time dilation

The radar antenna on a navy ship rotates with an angular speed of 0.22 rad/s. What is the angular speed of the antenna as measured by an observer moving away from the antenna wth a speed of 0.62c?

### Maxwell's speed distribution law

(See attached file for full problem description with diagram and symbols) --- 1) Find the fractional number of molecules of a gas having speeds between vm and 1.05vm where vm = Sq.root(2kT/m) and is denoted as the most probable speed. [vm denotes v subscript m] 2) At what radial "distance" v from the origin of velocity

### Period of small oscillation of sphere rolling in cylinder

A solid sphere is rolling without slipping on a vertical circular ramp with radius R. The sphere has radius r and mass m with a moment of inertia I = (2/5)m r^2. Find the period of a small amplitude oscillation. (See attached file for full problem description with diagram and equations)

### Spaceship rotation problem

A 20-meter-long spaceship is drifting in space, and is in the orientation shown below left, initially not spinning at all. The pilot needs to get the spaceship turned around 180 degrees, with the positions of the nose and tail switched around, as shown below right. To accomplish this, he fires a pair of small identical rocket

### Rate of rotation of a collapsed star

A star rotates about its axis through a diameter once in 50 days. At the end of its life the star collapses to one hundredth of its orginal diameter. What will the rate of rotation of the collapsed star be?

### Problems 4.19 & 4.21 from 'Introduction to Elementary Particles' by David Griffiths

Problems 4.19 & 4.21 from 'Introduction to Elementary Particles' by David Griffiths. See attached file for full problem description.

### Waves, Heat and Light 300 level in Undergraduate

2. Walking the dog - On your way to class you might have noticed that everyone was walking at more or less the same speed. In this question we will explore the reason for that. a) First, consider the leg as a physical pendulum, write down an expression for the natural angular frequency of oscillation of a simplified model fo

### Angular acceleration

A merry-go-round makes 60 revolutions in a 10.0 minute (600 seconds) ride. (a) What is the agular speed w(omega) in rad/sec? (b) What is the tangential speed of a person sitting 5.0 m from the center (axis of rotation)? (c) What centripetal acceleration does the person in part b have? (d) If the person's mass is 50 kg

### How much work must be supplied to get the record to rotate at this speed, and what supplies the work?

A 0.050kg phonograph record with a radius of 0.15m drops onto a turntable and is soon rotating at 33 1/3 rpm. How much work must be supplied to get the record to rotate at this speed, and what supplies the work?

### Rotation: Tipping or sliding.

I have a 72" tall air-compressor that weights 120 pounds with a 20" base. I have a cart that is 36"wx72"l the surface of the cart where the compressor will be mounted is 10" off the ground. The cart wheels are in the corners, it is rated to carry 3600 pounds and weights 114 pounds. If the compressor is placed centered on the car

### Magnetic effects of Current: Field, force, induction

1) The figure (*see attachment) shows 11 paths through a region of uniform magnetic field. One path is a straight line; the rest are half circles. The table (*see attachment) gives the masses, charges and speeds of the 11 particles that take these paths through the field in the direction shown. Which path corresponds to which pa

### Moment of Inertia Tensor

Calculate the moment of inertia tensor for a solid hemisphere for rotation about its center of mass.

### Tangential Speed and Acceleration

A helicopter blade has an angular speed of 6.50 rev/s and an angular acceleration of 1.30 rev/s^2. Find the magnitudes of the tangential speed and acceleration for a point (a) 3.00m from the center of rotation and (b) a point on the blade 6.70 m from the center of rotation.

### What is the force needed for circular motion?

A spring scale on a rotating platform indicates that the horizontal force on a 0.452 kg mass is 1.34N when the mass is 2.37m from the axis of rotation. How long does it take for the platform to make on revolution?

### Force of Rod on Particle

See attachment for picture. The particle has a mass of 0.5kg and is confined to move along the smooth horizontal slot due to the rotation of the arm OA. Determine the force of the rod on the particle and the normal force of the slot on the particle when theta = 30 deg. The arm has an angular acceleration of theta** = 3 rad/s

### Center of percussion-center of mass

A baseball bat rests on a frictionless, horizontal surface. The bat a length of 0.900m, a mass of 0.800 kg, and its center of mass is 0.600m from the handle end of the bat. ThE MOMENT OF INERTIA OF THE BAT ABOUT ITS CENTER OF MASS IS 0.0530kg*m^2 The impact applies an impulse : J= integral from t2 to t1 of F*dt. at a po

### Unwinding Cylinder (Moment of Inertia; Angular Rotation)

A cylinder with moment of inertia I about its center of mass, mass m, and radius r has a string wrapped around it which is tied to the ceiling. The cylinder's vertical position as a function of time is y(t). At time t=0 the cylinder is released from rest at a height h above the ground. **Please see attachment for complete q

### Angular Speed - Rotational Kinematics

Learning Goal: To understand the meaning of the variables that appear in the equations for rotational kinematics with constant angular acceleration. Rotational motion with a constant nonzero acceleration is not uncommon in the world around us. For instance, many machines have spinning parts. When the machine is turned on or o

### Rotation of a Rigid Body

An electric ceiling fan is rotating about a fixed axis with an initial angular velocity of 0.200 rev/s . The angular acceleration is 0.911 rev/s^2 . Its blades form a circle of diameter 0.720m . a) Through how many revolutions has the blade turned in the time interval 0.201s? b) What is the tangential speed v_tan (in m/s) of

### Calculating the Resultant Force of a Ride

Question: In an amusement park ride called The Roundup, passengers stand inside a 19.0m diameter rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane, as shown in the figure (see attachment). A. Suppose the ring rotates once every 4.70s. If a rider's mass is 52.0kg, with how much force

### Electromagnetics Problems

1. The flux in a single-loop coil of area 37 cm^2 steadily changes from 6.5 x 10^-3 T to 9.3 x 10^-3 T in 0.50s. What emf is induced in the coil? 2. A wire coil of 25 turns has a cross-sectional area of 10 cm^2. The coil is placed in a uniform field of large magnet with B=0.20 T. The coil is suddenly rotated 90 degrees from a