Rotational kinetic energy Definition and 140 Threads

I have a question regarding angular momentum and rot kinetic energy. For example, if angular momentum is conserved, and the radius is cut in half, then moment of inertia is reduced by a fourth, which will result in increase in angular velocity by factor of 4. My question is why is the...

Homework Statement Engineers are designing a system by which a falling mass m imparts kinetic energy to a rotating uniform drum to which it is attached by thin, very light wire wrapped around the rim of the drum. There is no appreciable friction in the axle of the drum, and everything starts...

Homework Statement You attach a mass M to a string and wind the string around the circumference of a wheel. The wheel has two hubs with radii R1 and R2 with R2 > R1. You perform two experiments. First you wind the string around the smaller radius wheel and allow the mass to fall a distance...

A string is wrapped around a disk of mass 2.1 kg (it's density doesn't have to be uniform). From rest, you pull the string with a constant force of 9 N. At this instant, the center of mass has moved 0.11 m, and your hand has moved 0.28 m. 1. At this instant, how much rotational kinetic...

Homework Statement I have a wheel with a diameter of 1.4m and the radius of gyration is 0.42m. The wheel has a mass of 13kg. Calculate maximum rotational kinetic energy. Homework Equations The Attempt at a Solution From this all i can do is calculate the moment of inertia which...

1. I'm doing an experiment where I have a brass hollow cylinder, and I roll it down an inclined plane, and after each trial, I add fish weights to the inside of it to increase the mass. I'm testing the proportionality between mass and angular velocity, with my hypothesis being an inverse...

Homework Statement The picture shows an overhead view of a ring that can rotate about its center like a merry-go-round. Its outer radius R2 is 0.7 m, its inner radius R1 is R2/2, its mass M is 7.3 kg, and the mass of the crossbars at its center is negligible. It initially rotates at an angular...

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...

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...

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.

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...

A simple rotating system with no external forces acting on it carries a fixed angular momentum and an associated rotational kinetic energy. If the system changes its internal configuration, such as a spinning skater retracting or extending his/her arms, the angular momentum remains constant...

Homework Statement The moment of inertia of a fly wheel about it's axis is 20 kg m2. A constant torque of 40 N m is applied to the initially stationary fly wheel. Find it's rotational KE after 3 seconds assuming there is no friction in the system? Homework Equations...

Hi, I was wondering if the formula for rotational energy: E = 1/2 * L * w where L is the angular momentum and w is the angular velocity, is actually correct for relativistic velocities. Using L = p * r and w = v / r where p = the linear momentum = m * v We get...

Homework Statement A solid sphere with a mass 8.2kg and radius 10cm is sliding along a frictionless surface with a speed 5.4m/s while at the same time spinning. The sphere has 0.31 of its total kinetic energy in translational motion. How fast is the sphere spinning? Homework Equations...

Homework Statement There is a system consisting of two masses, m1=20 kg, m2=30kg on a pulley and m2 is 2 meters above the ground, while m1 is on the ground. This is the question: the system released from rest a 30 kg block that is 2m above a ledge. The pulley is a disk with radius of 10 cm...

Homework Statement The four particles shown below are connected by rigid rods of negligible mass where y1 = 6.60 m. The origin is at the center of the rectangle. The system rotates in the xy plane about the z axis with an angular speed of 5.40 rad/s...

Homework Statement What is the rotational kinetic energy of Jupiter? Assume Jupiter is a uniform sphere with a rotational period of 9.81 hr. Homework Equations I= 2mr^2/5 Krot= I*omega^2/2 omega= 2pi/T The Attempt at a Solution i found the omega using the equation above and the...

Homework Statement Uniform density rod with mass 1.2 kg, length 0.7m rotates around an axis perpendicular to the rod, with angular speed 50 rad/sec. its center moves with a speed of 8m/s. What is the rotational kinetic energy? Homework Equations K= 1/2 I * V^2 (V is angular speed...

Homework Statement A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolutions per 8.00s? Assume it is a solid cylinder. Homework Equations \DeltaKE=Wnet=1/2(Iw2)=14211.7J...

Homework Statement A spool of wire mass m and radius r is unwound under a constant force F. Assuming that the spool is a uniform solid cylinder that does not slip, show that the acceleration of the center of the mass is 4F/3m Homework Equations F+f=ma f=ma-F \tau =I\alpha=Fr-fr...

Four children stand at the edge of a circular horizontal platform that is free to rotate about a vertical axis. Each child has a mass of 35 kg and they are at positions that are a quarter-circle from each other. The platform has a moment of inertia equal to 500 kg*m^2 and a radius of 2.0 m. The...

Homework Statement The three 280 g masses in the figure are connected by massless, rigid rods to form a triangle. What is the triangle's rotational kinetic energy if it rotates at 6.5 revolutions per s about an axis through the center? Values given: Mass of each ball at the corner of the...

Homework Statement A horizontal 800N merry go round of radius 1.50m is started from rest by a constant horizontal force of 50.0N applied tangetially to the merry go round. Find the kinetic energy of the merry go round after 3.00s. (assume it is a solid cylinder). Homework Equations I =...

A small diameter (2.00 mm), solid steel ball rolls from rest, without slipping, down a track and into a loop-the-loop of 1.50 meters diameter. Between the starting point on the track and the top of the loop the ball converts 10.0% of its initial mechanical energy into other forms of energy. From...

Homework Statement Assume the Sun is a uniform, rigid sphere (it is spherically shaped but actually is not of uniform density nor a rigid body). The Sun rotates once every 27 days. (a) Calculate the rotational kinetic energy of the Sun in joules. (b) The luminosity (power output) of the...

Homework Statement A 31.0 kg child runs with a speed of 2.80 m/s tangential to the rim of a stationary merry-go-round . The merry-go-round has a moment of inertia of 520 kg\cdot m^2 and a radius of 2.51 m. When the child jumps onto the merry-go-round, the entire system begins to rotate...

Homework Statement Crab Nebula releases energy at a rate of 5x1031 W, obtaining its energy from the rotational kinetic energy K of a neutron star at its centre. Period of neutron star's rotation = 0.0331s. T increases by 4.22 x 10-13s per second. What is the moment of inertia of the...

Homework Statement What is the ratio of the rotational kinetic energy of the Earth to the rotational kinetic energy of the Moon as they spin about their axes? The Attempt at a Solution Me = Mass of Earth (5.97 × 1024 kg) Re = Radius of Earth (6.37 × 106 m) Mm = Mass of Moon (7.35 ×...

Homework Statement A car is designed to get its energy from a rotating flywheel with a radius of 1.12 m and a mass of 736 kg. Before a trip, the flywheel is attached to an electric motor, which brings the flywheel’s rotational speed up to 7270 rev/min. Find the kinetic energy stored in the...

Homework Statement A bicycle has wheels of radius 0.25 m. Each wheel has a rotational inertia of 0.096 kg* m2 about its axle. The total mass of the bicycle including the wheels and the rider is 79 kg. When coasting at constant speed, what fraction of the total kinetic energy of the bicycle...

Two disks of identical mass but different radii (r and 2r) are spinning on frictionless bearings at the same angular speed ωo, but in opposite directions. The two disks are brought slowly together. The resulting frictional force between the surfaces eventually brings them to a common angular...

I don't remember learning this in my C Physics Mechanics class which is odd since it seems pretty important. In the case where you have one object colliding with another object off its center of mass, how do you tell how much of the energy from the collision goes into rotational kinetic energy...

Homework Statement For a physics lab we need to calculate the final linear velocity of a disc and hoop. The only thing we are given is the length and height of the ramp and the mass and radius of the disc and hoop. Homework Equations I thought before that with conservation of energy, I could...

Homework Statement A 16 g CD with a radius of 6.0 cm rotates with an angular speed of 42 rad/s. (a) What is its kinetic energy? Homework Equations k=1/2Iw^2 The Attempt at a Solution k=1/2(0.016x0.0036)(1764)=0.05 J

Homework Statement A car is designed to get its energy from a rotating flywheel with a radius of 1.90 m and a mass of 487 kg. Before a trip, the flywheel is attached to an electric motor, which brings the flywheel's rotational speed up to 5150 revolutions per minute. Find the kinetic energy...

Homework Statement A small sphere, with radius 1.6 cm and mass 5.2 kg, rolls without slipping on the inside of a large fixed hemispherical bowl with radius 0.82 m and a vertical axis of symmetry. It starts at the top from rest. What is the kinetic energy of the sphere at the bottom? What...

Homework Statement A dumbell made of two point masses separated by a massless rod of fixed length has centre of mass velocity V and rotates about its CM with angular velocity \omega. Two point masses m_1 and m_2 are located at r_1 and r_2 repsectivelt wrt the CM. Let T be the kinetic energy of...

Homework Statement (a) If R = 12 cm, M = 360 g, and m = 20 g (below), find the speed of the block after it has descended 50 cm starting from rest. Solve the problem using energy conservation principles. (Treat the pulley as a uniform disk.) Homework Equations KEi + PEi = KEf + PEf...

Homework Statement A 38.0 kg wheel, essentially a thin hoop with radius 1.13 m, is rotating at 280 rev/min. It must be brought to a stop in 15.0 s. (a) How much work must be done to stop it? Homework Equations change in KE = (1/2)Iwi^2 - (1/2)Iwf^2 I = (1/2)mr^2The Attempt at a Solution...

Is the Change in Rotational Kinetic Energy Frame Invariant? -------------------------------------------------------------------------------- I know the translational kinetic energy of an object is frame dependent. That is, in the center of mass frame of the object, the kinetic energy is...

When talking about the translational velocity of a rigid body in physics, the velocity is always frame dependent, and therefore, the translational kinetic energy is frame dependent. But does this apply to angular rotation phenomenon? If in one frame, the angular velocity of a rigid body is 10...

Homework Statement A wheel (solid cylinder), mass of 13 kg and radius of 0.33m is initially at rest. The wheel undergoes an angular acceleration of 5 rad/s^2 for 18 seconds, rotating about its center axis (no translation). Find the Kinetic energy of the wheel at the end of the 1 seconds...

Homework Statement A skater spins with an angular speed of 17.4 rad/s with his arms outstretched. He lowers his arms, decreasing his moment of inertia from 43 kg/m^2 to 37 kg/m^2. Calculate his initial and final rotational kinetic energy. Homework Equations L=I\omega KE=1/2I\omega^2...

Homework Statement A grinding wheel in the shape of a solid disk is 0.240m in diameter and has a mass of 2.50kg. The wheel is rotating at 2050rpm about an axis through its center. What is its kinetic energy? How far would it have to drop in free fall to acquire the same amount of kinetic...

Homework Statement A uniform rod AB is hinged smoothly at A. The length L of the rod is 50cm. Determine a) The angular velocity, of the rod when it makes an angle (Theta) =30o with the verticle. ( Moment of inertia of rod about axis through one end and perpendicular to the rod = 1/3...

Homework Statement A uniform spherical shell of mass M = 7.70 kg and radius R = 0.670 m can rotate about a vertical axis on frictionless bearings. A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 0.0880 kg·m2 and radius r = 0.0790 m, and is...

Hi, Suppose I am trying to find the work done in bringing a resting cylinder to an angular speed of 8 rad/s. Why is it INCORRECT to find the corresponding tangential velocity at a point on the outer surface of the cylinder (using angular speed * radius = tangential speed) and use the...

Homework Statement An airplane propeller is 2.02 m in length (from tip to tip) with mass 127 kg and is rotating at 2300 rpm about an axis through its center. You can model the propeller as a slender rod. a)What is its rotational kinetic energy? b)Suppose that, due to weight constraints, you had...

Homework Statement The Earth can be approximated as a sphere of uniform density, rotating on its axis once a day. The mass of the Earth is 5.97×10^24 kg, the radius of the Earth is 6.38×10^6 m, and the period of rotation for the Earth is 24.0 hrs. What is the moment of inertia of the...