Rotational Definition and 1000 Threads

A rotation is a circular movement of an object around a center (or point) of rotation. The geometric plane along which the rotation occurs is called the rotation plane, and the imaginary line extending from the center and perpendicular to the rotation plane is called the rotation axis ( AK-seez). A three-dimensional object can always be rotated about an infinite number of rotation axes.
If the rotation axis passes internally through the body's own center of mass, then the body is said to be autorotating or spinning, and the surface intersection of the axis can be called a pole. A rotation around a completely external axis, e.g. the planet Earth around the Sun, is called revolving or orbiting, typically when it is produced by gravity, and the ends of the rotation axis can be called the orbital poles.

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  1. L

    Find Maximum mass with the principles of torque and rotational equilibrium

    I need help with this physics problem! Please help I'm completely stuck. A beam 3m long is free to pivot up and down about the end attached to a wall. The mass of the beam is 25 kg and the cable supporting the beam can support a maximum force of 1800 N. What is the maximum mass that a man...
  2. A

    Spinning puck rotational motion

    Homework Statement A puck, mass m, on the end of a (thin, light) string rotates in a circle of radius r_0 at a speed v_0 on a frictionless table. The radius of the circle is slowly reduced from its initial value by pulling the string through a hole in the table. A. Hence write down an...
  3. C

    Rotational kinematics of a turntable

    Homework Statement An electric turntable 0.710 m in diameter is rotating about a fixed axis with an initial angular velocity of 0.230 rev/s. The angular acceleration is 0.887 rev/s^2. A. Compute the angular velocity after a time of 0.192 s. B. Through how many revolutions has the blade...
  4. QuarkCharmer

    Ball down hill w/ rotational motion

    Homework Statement A solid ball is released from rest and slides down a hillside that slopes downward at an angle 69.0 degrees from the horizontal. What minimum value must the coefficient of static friction between the hill and ball surfaces have for no slipping to occur? Homework Equations...
  5. M

    Rotational dynamics (rolling friction)

    problem 1: Homework Statement this isn't quite a problem but a general confusion about how to setup the problem. for example: a cylinder of radius R with mass M has a force T applied at its center of mass, pointing horizontally to the right. assuming the cylinder only rolls without...
  6. L

    Rotational motion, energy conservation problem

    rotational motion, energy conservation problem URGENT please help Homework Statement A uniform rod of mass M=2 kg and length L = 2m is pivoted from its end. It has a point mass m=1 kg on its tip. It stars from rest at an angle of 30 degrees above horizontal. It falls under the influence of...
  7. J

    Rotational & rolling energy, springs help

    Homework Statement There are a few, help with any would be appreciated. A 16,000 kg F-18 (jet fighter) lands at 52 m/s on an aircraft carrier, its tail hook snags the cable to slow it down. The cable is attached to a spring with a spring constant of 60,000 N/m. How far does the spring...
  8. khurram usman

    Centripetal and tangential acceleration in rotational motion ?

    centripetal and tangential acceleration in rotational motion...? consider a stone attached to a string moving in a horizontal circle in a gravity field. now it has two accelerations one along the \hat{r} direction and the other along \theta\hat{} (theta hat) direction but there is only one...
  9. L

    Rotational Kinematics Football Problem

    Homework Statement A quarterback throws a pass that is a perfect spiral. In other words, the football does not wobble, but spins smoothly about an axis passing through each end of the ball. Suppose the ball spins at 9.0 rev/s. In addition, the ball is thrown with a linear speed of 21 m/s at an...
  10. S

    Rotational Mechanics Problem (Rotating solid wooden disk)

    I have the working for part d) but I don't understand certain parts, so my problems lie with part d), f) and g) Homework Statement 3. A solid wooden disk is suspended as shown: it has mass 7.70 kg and radius 0.219 m . It is rotated from rest about its vertical axis, reaching an angular...
  11. M

    Translational kinetic energy vs. rotational kinetic energy

    Homework Statement My question relates to a physics problem dealing with the orbit of a moon. In the problem, the orbit of the moon shrinks such that its radius to the center of the planet in question (here, Earth) is smaller. The question gives a great deal of information, but at one point...
  12. C

    Calculating force of friction with torque, rotational inertia and angular accel

    Homework Statement I have a plot whose vertical intercept is 0.00352 [Nm] If the bearings are 2 [mm] from the center of the wheel, then what is the force of friction? Use three significant figures for your answer in Newtons. Homework Equations Torque= (Rotational Inertia)(Angular...
  13. T

    Kinetic and potential energy in circular and rotational motion

    Homework Statement Consider a bead of mass m that is confined to move on a circular hoop of radius r. The axis of symmetry of the hoop is horizontal, and the hoop is rotating about a vertical axis at a uniform rate \omega. Neglect friction and assume a constant gravitational acceleration of...
  14. M

    Rotational Statics Of A Balance Beam

    Homework Statement A gymnast with mass m1 = 48 kg is on a balance beam that sits on (but is not attached to) two supports. The beam has a mass m2 = 121 kg and length L = 5 m. Each support is 1/3 of the way from each end. Initially the gymnast stands at the left end of the beam. 1)What is the...
  15. M

    Rotational And Translational Motion Of A Bowling Ball

    Homework Statement A spherical bowling ball with mass m = 3.4 kg and radius R = 0.115 m is thrown down the lane with an initial speed of v = 8.5 m/s. The coefficient of kinetic friction between the sliding ball and the ground is μ = 0.27. Once the ball begins to roll without slipping it moves...
  16. G

    Calculating Rotational Speed of Car Tyres: How Many Spins in a Given Distance?

    Rotational Speed of Car tyre? hey guys i was trying to figure out this rotational speed of car tyre?...i have with me the diameter of the car tyre and the distance which it is traveling and the length of the car...so can anyone help? i need to find out how much times will the tyre spin and at...
  17. M

    Rotational Motion and Law of Gravity

    a) Two objects attract each other with a gravitational force of magnitude 9.30 x10-9 N when separated by 19.4 cm. If the total mass of the objects is 5.06 kg, what is the mass of each? Heavier mass_______kg Lighter mass______ kg my attempt: F=Gm1m2/r^2 so I rearranged to get m1 and m2...
  18. H

    Kinetic and Rotational energy of a sphere

    Hi guys so this is my first time posting a question on this amazing forum, i hope i am doing this right since i read that no one will help me if i am missing something. Anyways, i am dealing with a physics problem that it driving me crazy (mainly because my teacher does not explain anything!)...
  19. V

    Speed of Objects Rolling and Sliding Down a Hill

    Homework Statement A solid uniform marble and a block of ice, each with the same mass, start from rest at the same height H above the bottom of a hill and move down it. The marble rolls without slipping, but the ice slides without friction. Find the speed of each of these objects when it...
  20. W

    Rotational Kinematics Time Problem

    Homework Statement A spinning wheel on a fireworks display is initially rotating in a counterclockwise direction. The wheel has an angular acceleration of -4.40 rad/s^2. Because of this acceleration, the angular velocity of the wheel changes from its initial value to a final value of -24.0...
  21. A

    Rotational Kinematics-Vinyl Record

    1. In the “old days”, long before CD’s and MP3’s, people listened to music using vinyl records. Long-playing vinyl records spin at a constant rate of 33-and-one-third rpm (revolutions per minute). The music is encoded onto a continuous spiral track on the record that starts at a radius of 30 cm...
  22. 1

    Rotational Inertia worked it many times.

    Homework Statement In the figure below, the pendulum consists of a uniform disk with radius r = 10 cm and mass 480 g attached to a uniform rod with length L = 500 mm and mass 260 g. Homework Equations The Attempt at a Solution I'm going to cut to the chase. I'm basically...
  23. P

    Rotational Motion change angular rotational

    Homework Statement 9. A force can change angular rotational if it acts through: a. the axis of rotation *b. a lever arm tangential to the direction of rotation c. a moment arm parallel to the axis of rotation d. none of these Homework Equations n/a The Attempt at a...
  24. P

    Rotational Motion maximum acceleration

    Homework Statement 7. A 130-kg refrigerator that is 2.30 m tall and 90.0 cm wide is being delivered by a truck. The center of gravity of the refrigerator is located at its geometrical center and the refrigerator is facing sideways in the truck and is prevented from sliding. What is the...
  25. P

    Rotational Motion Speed at the top of the loop

    Homework Statement 12. A motorcycle travels around a vertical 12 m radius loop. What is its speed at the top of the loop if the normal force exerted by the seat on the driver is equal to ¼ of his weight? a. 7 m/s b. 8.1 m/s *c. 9.4 m/s d. 15 m/s e. 88 m/s Homework Equations...
  26. P

    Rotational Motion angular speed

    Homework Statement 11. A wheel with an angular speed of 2.0 rad/s is rolling on a horizontal surface and starts down a ramp. It rolls down the ramp with a constant angular acceleration of 2.5 rad/s2. If it takes 8 s to reach the bottom of the ramp, what is the final angular speed of the...
  27. P

    Rotational Motion Tension at the bottom of the circle

    Homework Statement 9. A 0.61 kg mass attached to the end of a 0.50 m cord rotates in a vertical circle. The angular speed of the mass at the bottom of the circle is 2π rad/s. The tension in the string at this point is: a. 18 N b. 21 N c. 12 N *d. 54 N Homework Equations W=mg F=ma...
  28. P

    Rotational Motion maximum speed

    Homework Statement 3. A 1500 kg car is moving on an un-banked curve with a radius of 98 m. The coefficients of static and kinetic friction are 0.73 and 0.50 respectively. The maximum speed the car can move without skidding is: *a. 27 m/s b. 22.4m/s c. 21 m/s d. 30 m/s e. none...
  29. X

    Rotational Momentum Problem Help

    A ballistic pendulum consists of an arm of mass M and length L = 0.55 m. One end of the arm is pivoted so that the arm rotates freely in a vertical plane. Initially, the arm is motionless and hangs vertically from the pivot point. A projectile of the same mass M hits the lower end of the arm...
  30. J

    Understanding Rotational Motion: Answers for Jade

    Okay so my mechanics teacher is taking a rather mathematical approach to CM and its really confusing me. Can someone explain to me what this actually means? d hat{r}/dt=dot{theta} hat{theta} and d hat{theta}/dt=-dot{theta} hat{r} I mean I know that anything with a hat on top is a...
  31. V

    Problem in choosing axis in rotational mechanics?

    In rotational mechanics i am mostly confused with the axis of rotation. Let me give you some examples of question. about which axis. Is that instantaneous axis of rotation. OK this may seem to be solved here but what about this question. Now once again. which axis should i choose...
  32. L

    Gravitational potential energy and rotational motion

    Homework Statement A marble is placed at the top of an inverted hemispherical bowl of radius R = 0.30 m. It starts from rest and slides down the bowl without friction. Draw a free body diagram when the marble reaches an angular position θ = 16.6°. From your FBD, sketch the approximate...
  33. S

    Rotational Dynamics of a Bicycle wheel

    Homework Statement A bicycle wheel has a diameter of 63.8 cm and a mass of 1.79 kg. Assume that the wheel is a hoop with all of the mass concentrated on the outside radius. The bicycle is placed on a stationary stand and a resistive force of 117 N is applied tangent to the rim of the tire...
  34. F

    Rotational Dynamics Equilibrium - Torque With PICS

    Homework Statement ** disregard A) http://img153.imageshack.us/img153/917/img20111024001591.jpg Homework Equations T= Fd The Attempt at a Solution [PLAIN][PLAIN]http://img21.imageshack.us/img21/9645/img20111024001611.jpg Basically I'm stuck now, and don't know what to do.. I...
  35. J

    Does Spin have rotational kinetic energy?

    I have two questions regarding rotational kinetic energy. I know that rotational kinetic energy is defined as: KE = ½ I Ω^2 Where KE is the rotational kinetic energy [in units of: joules; kg*m^2/s^2], I is the Moment of inertial [in units of: kg* m^2], and Ω is angular velocity [in units...
  36. C

    Condition of rotational equilibrium in circular motion

    Homework Statement Consider a cyclist turning around a circular track with radius r and speed v as shown in attached fig. Let W be the weight of the system (cyclist + bicycle) (W = mg) N = normal force by ground on the system f = static friction by ground on the system θ = angle of...
  37. F

    Optimizing Arm Design for Maximum Strength: Insights from Nature's Creations

    Homework Statement How could mother nature have improved on our arm design so that we could lift larger loads? Homework Equations None. The Attempt at a Solution I really don't understand how our arm design could be improved. Perhaps our pivot point was moved must torque be maximized? I'm...
  38. C

    Finding radius of satellite in orbit given mass and rotational period

    Homework Statement Suppose that Captain Omega of the Imperial Space Patrol wishes to place a spy satellite in geosynchronous orbit above the mysterious Planet X, which has a mass of 5.90 x1024 kg, and a rotational period of 26.4 hours. (a) What should be the radius of the satellite's orbit...
  39. LarryS

    Does Spin Have Rotational Kinetic Energy?

    Say we have an uncharged particle of spin ½ that is at rest. Of course, there is an energy associated with the particle’s rest mass. But is there an additional (rotational kinetic) energy associated with it’s spin? As always, thanks in advance.
  40. E

    Calculating Kinetic Energy with Rotational Motion

    Homework Statement A student sits at rest on a piano stool that can rotate without friction. The moment of inertia of the student-stool system is 3.6 kg·m2. A second student tosses a 1.7 kg mass with a speed of 3.0 m/s to the student on the stool, who catches it at a distance of 0.38 m from...
  41. 1

    How Do You Calculate the New Angular Speed of Coupled Wheels?

    Homework Statement I really don't understand what to do next. A wheel is rotating freely with an angular speed of 950rev/min on a shaft whose rotational inertia is negligible. A second wheel, initially at rest and with twice as much rotational inertia of the first is suddenly coupled on...
  42. G

    Why Is My Solution for Rotational Motion Incorrect?

    Homework Statement Please see the attachment. Homework Equations The Attempt at a Solution Please see the attachment. When I tried to solve the equations for a I got a different answer and I don't see what I'm doing wrong. Please let me know if you cannot follow my work...
  43. G

    Rotational Motion: Understanding Net Force and Torque

    Homework Statement See attachment Homework Equations The Attempt at a Solution I'm confused as to why it's Ʃ F = m a = 20 + f as opposed to Ʃ F = m a = 20 - f Also when it states the net torque Ʃ torque = I alpha = ( 20 - f ) ( 0.10 ) = 0.02 ( a / 0.10 ) Why is...
  44. M

    How Do You Calculate the Components of Acceleration for a Car on a Curved Track?

    A car is traveling around a horizontal circular track with radius r = 270 m at a constant speed v = 17 m/s as shown. The angle θA = 23° above the x axis, and the angle θB = 58° below the x axis. 1. What is the x component of the car’s acceleration when it is at point A? 2.What is the y...
  45. G

    What is the Moment of Inertia of the Pulley?

    Homework Statement See first attachment Homework Equations The Attempt at a Solution a = r * alpha r = a / alpha If I think of the whole pulley as a system... Ʃ F_sys = m_sys*a = Fg_1 - Fg_2 I called the 2 kg block, block 1, I called the 1.8 kg block block 2. a = [...
  46. S

    Physics problem involving rotational motion.

    Homework Statement The question is given in the following pictures. http://imageshack.us/photo/my-images/851/iitjee2011.png/ http://imageshack.us/photo/my-images/844/iitjee20112.png/ This question had one or more than one correct answer(s). This was asked in IIT-JEE 2011 (which is...
  47. G

    Easy Rotational Motion Question

    Homework Statement A grindstone has a moment of inertia of 1.6*10^-3 kg m^2. When a constant torque is applied, the flywheel reaches an angular velocity of 1200 rev/min in 15 s. Assuming it started from rest, find (a.) the angular acceleration; (b.) the torque applied; (c.) the angle...
  48. S

    Can Sliding Friction Affect a Rolling Disk?

    Homework Statement a disk is rolling on a flat horizontal surface.only rolling friction will act on the body.(true/false).ans false WHY?a body rolls.therefore sliding friction can't act on body.(true/false).ans. false WHY? Homework Equations The Attempt at a Solution since the...
  49. M

    Solving Rotational Matrix: 6 Parameters from 3 Angles

    The Scenario: We have a frame 1 and a frame 0. The frame 0 is rotated in some manner, but not translated so their share an point of origin. I have 3 angles between different axes of the different frames. I am suppose to describe the orientation of frame 0 in frame 1 with an 3x3 rotation...
  50. A

    Simple bug on uniform rod rotational momentum problem

    Homework Statement A small 10.0-g bug stands at one end of a thin uniform bar that is initially at rest on a smooth horizontal table. The other end of the bar pivots about a nail driven into the table and can rotate freely, without friction. The bar has mass 60.0g and is 90cm in length...
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