Rotational Definition and 1000 Threads

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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.

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...

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...

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...

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...

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...

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 = [...

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...

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...

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...

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...

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...

Homework Statement A block with mass m is revolving with linear speed v1 in a circle of radius r1 on a frictionless horizontal surface (see the figure ). The string is slowly pulled from below until the radius of the circle in which the block is revolving is reduced to r2. Calculate the...

Homework Statement A 45.0-cm diameter wheel, consisting of a rim and six spokes, is constructed from a thin rigid plastic material having a linear mass density of 25.0 g/cm. This wheel is released from rest at the top of a hill 52.0m high. a.) How fast is it rolling when it reaches the...

One more question on rotation. first of all see attachment i want to say that if friction is too large then net force is in direction of inclined in upward direction but from common experience we can say that it will move in downward direction so where is it going wrong. why it moves in...

Homework Statement If two circular discs A and B of mass m and 3m and radii R,2R, respectively. are placed from the top of a rough inclined plane, which disc will reach bottom first.2. The attempt at a solution NOTE: u is coefficient of friction (both kinetic and static). g is acceleration due...

So every mountain biker or motocross rider knows to never grab the front brake in the air. When you do the front end drops and can potentially ruin your day in a hurry. I figure that due to the loss of rotational inertia gravity accelerates the front wheel more rapidly, but I would like to see...

Homework Statement A cubical block of mass 'm' and edge length 'a' slides down a rough inclined plane of inclination alpha radian with a uniform speed. Find the torque of the normal[/color] force acting on the block about its center. On the back of the book answer is \frac{1}{2}mga...

Homework Statement Summary: The pulley in the figure has radius (R) and a moment of inertia (I). The rope does not slip over the pulley, and the pulley spins on a frictionless axle. The coefficient of kinetic friction between block A and the tabletop is \muk. The system is released from...

Can anybody please explain to me the concept of rotational motion?? I'm so lost in that chapter... ><

Homework Statement A thin uniform rod of mass (M) and length (L) is bent at its center so that the two segments are now perpendicular to each other. a. Find its moment of inertia about an axis perpendicular to its plane and passing through the point where the two segments meet...

There are several references to “lost” kinetic energy when trying to analyze motion based on the Conservation of Momentum and the Conservation of Energy laws. Generally, the answer to apparent discrepancies include references to ‘elastic’ or ‘in-elastic’ collisions and whether or not they are...

The moon has a diameter of 3.48 x 10^6 m and is a distance of 3.85 x 10^8m from the earth. The sun has a diameter of 1.39 x 10^9 m and is 1.50 x 10^11 m from the earth. (a.) What are the angles (in radians) subtended by the moon and the sun, as measured by a person standing on the earth...

A jet is circling an airport control tower at a distance of 18.0 km. An observer in the tower watches the jet cross in front of the moon. As seen from the tower, the moon substends an angle of 9.04 x 10-3 radians. Find the distance traveled (IN METERS) by the jet as the observer watches the nose...

I don't know if I'm using the terms properly, since I am no mechanical engineer, but I am attempting to find the best way to convert rotational work from an electric motor to draw a long, high-torque linear stroke, followed by a very fast return stroke. To clarify my question, I trying to...

Homework Statement The equilibrium separation of the atoms in H35CI equals 1.27 x 10-10m. Calculate the energy separation between adjacent lines in the rotational-vibrational spectrum Homework Equations E = (n + 1/2)h\omega + h2/ 2I * l(l+1) I = \mur02 \mu = m1m2/ m1 + m2 The...

The Earth's rotational velocity at the Equator is 1,674.4 km/h or 465.1 m/s. The stars at the equator rotate at that same rate taking in account Precession at that particular time of the year and the longitude & latitude they are viewed from. Do the stars at the poles rotate faster then at the...

Homework Statement Why, for any system that is in rotational equilibrium, the torque about 1) any point on the object or 2) any point in space, must be zero.Homework Equations N/AThe Attempt at a Solution What I do not understand is, why the torque about ANY point on the object is zero...

For my investigation regarding the aerodynamic forces on a spherical projectile, I really need to know the theoretical ratio of rotational kinetic energy to linear kinetic energy of a spherical projectile (assuming the only spin is forward spin and there is no Magnus effect). Can someone please...

So the question is this: A disc is released from rest. A block is causing it to rotate. After a time t the block has fallen a height h and the disc has rotated through an angle theta. (in rad) Express h in terms of r (the radius of the part of the hub around which the string is wound) and...