Answered: The radius of gyration of a disc of…

The radius of gyration of a disc of mass 100 gm and radius 5 cm about an axis passing through its centre of gravity and perpendicular to the plane is-

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter8: Central-force Motion

Section: Chapter Questions

Problem 8.24P

See similar textbooks

Related questions

Q: A pulsar may form when a star of medium mass dies. On July 4, 1054 CE, Chinese astronomers witnessed…

Q: Certain neutron stars (extremely dense stars) are believed to be rotating at about 1.9 rev/s. If…

A: We know:

Q: A space station in a science fiction novel consist of a circular tube that will rotate about its…

A: Artificial gravity can achieved by this method for this we need ultra high source of power.…

Q: The directions of the tangential acceleration and velocity are always * perpendicular to each other.…

Q: 2. radius of gyration of a solid sphere rotating about its diameter if its radius is 5.0 cm A. O…

Q: Assuming the earth to be an oblate spheroid, so that the distance from the center to the equator is…

Q: . The radius of the earth's orbit around the sun is 1.5 x 1011m. Calculate the angular and liner…

A: Time period, T = 365 days = 365×24×60×60 s Radius, r = 1.5×1011 m

Q: Suppose a star the size of our Sun, but with mass 5.0 times as great, were rotating at a speed of…

A: Introduction: Here in this problem we use conservation of angular momentum. For system of masses⇒…

Q: Assume that the answer is between 90 and 270 degrees.What is the arctangent of -8.144?

A: We know that value of tan in third quadrant is positive. hence the angle can not lie in the third…

Q: Priya is sitting on the edge of a horizontal circular plateform of radius 6m rotating with constant…

A: Velocity of Priya with respect to Rahul = 1 m/s

Q: Calculate the speed at the edge of a disc of radius 7 cm that rotates at the rate of 5 rev/s. Answer…

A: radius of disc (r) = 7 cm= 0.07 m angular speed (ω) = 5 rev/s=5×2π rad/s= 31.4 rad/s

Q: the angular velocity of a particular moving in a circle of radius 2m is increased in 5 minutes from…

Q: a horizontal plane about an axis -A thin uniform circular disc of mass M and radius R is rotating…

Q: Although their linear motions vary linearly with their distances from the axis of rotation, all…

Q: •• The Sun, with Earth in tow, orbits about the center of the MilkyWay galaxy at a speed of 137…

Q: The apparent weight of passengers at the rim of a rotating space station is 73.1% of their actual…

A: Given data: Apparent weight is: Wa = 73.1% of Wactual = 0.731Wactual Distance of rim from its centre…

Q: A star rotates in a circular orbit about the center of its galaxy. The radius of the orbit is 2.9 x…

Q: A rubber ball with a radius of 3.2 cm rolls along the horizontalsurface of a table with a constant…

A: The determine the constant acceleration of the motion for the position as a function time is,

Q: A space station in a science fiction novel consists of a circular tube that will rotate about its…

Q: A disk with velocity v= 10m/s, mass m=4 kg, and radius r=.3 m. Find the total kinetic energy.

A: The total kinetic energy is the sum of the translation kinetic energy and rotational kinetic energy.…

Q: The figure above shows a small sphere of mass m at a height H from the center of a uniform ring of…

Q: Out of aphelion and perihelion , where is the speed of the Earth more and why?

A: Aphelion is the positon of the Earth from which it is most distant from the Sun and the perihelion…

Q: How many rotations do they go through while decelerating?

A: Wf2 - Wi2 = 2αθ Wf = Final annual speed =0 rad/s Wi = intial angular speed = 600rpm = 600×2π/60…

Q: At 714 A.M. on June 30, 1908, a huge explosion occurred above remote central Siberia, at latitude…

A: When looking downward at the north poll, it seems the rotation of the Earth is longitudinally at…

Q: What is the magnitude of angular momentum of JUST the partical circled to the system's mass center?

A: Mass of each particle (m)=0.5 kg Angular velocity of the body (ω)=2 rad/s Distance of the circled…

Q: A wheel of radius 0.34 m slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How…

A: Answer 53.832rev rotations does the wheel go through during this accleration.…

Q: Calculate the ratio of radii of gyration of a circular ring and a disc of the same radius with…

A: TO EXPLAIN: Calculate the ratio of radii of gyration of a circular ring and a disc of the same…

Q: A disk with velocity v= 10m/s, mass m=5 kg, and radius r=2 m. Find the total kinetic energy.

A: We know that for a disc: Inertia(I) is as below. value of the rotational kinetic energy is: value…

Q: d from the eq

Q: Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down…

Q: Calculate the angular momentum of mass 15 kg in an elliptical orbit of dimensions 10 cm and 20 cm…

Q: Does the center of gravity coincide with the fulcrum? Why?

A: Usually not, however, on uniform materials it can. For instance on a meter stick. There may be two…

Q: 5.3 Space Station Precession The space station precesses axis at a rate of one out the ny volution…

A: We are given the velocity for rotation about ny as, Np= 160RPMand radius of…

Q: If small particle 'm' is placed a distance 'x' from the central axis of a solid disk of total mass M…

Q: Calculate the coriolis force on a mass of 50g placed at a distance of 10cm from the axis of rotating…

A: The formula of Coriolis force (FC), FC = 2m( v × ω) v = ω × R FC = 2m( ω2R) Where, m = mass v =…

Q: A car whose wheels are 30 cm in radius is travelling with a constant velocity of 110 kph. If it is…

A: Given: The initial velocity of the car is 110 kph. The radius of the wheel is 30 cm = 0.3 m. The…

Q: A car whose wheels are 30 cm in radius is travelling with a constant velocity of 110 kph. If it is…

Q: A wheel of radius 4.4 cm is rotating at 600 radians per second. The linear velocity of particle at…

Q: A seat on the perimeter of a Ferris wheel at the amusement park experiences an angular displacement…

A: radius of the wheel, r= 20 mangular displacement, θ=37°( to find arc length, angle must be measured…

Q: Consider a star the size of our Sun (RSun = 696,340 km) , but with a 9.0 times greater mass that…

Concept explainers

Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.

Question

The radius of gyration of a disc of mass 100 gm and radius 5 cm about an axis passing through its centre of gravity and perpendicular to the plane is-

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Show that for eccentricity equal to one in Equation 13.10 for conic sections, the path is a parabola. Do this by substituting Cartersian coordinates, x and y, for the polar coordinates, r and , and showing that it has the general form for a parabola, x=ay2+by+c .
The Sun’s mass is 2.01030kg , its radius is 7.0105km , and it has a rotational period of approximately 28 days. If the Sun should collapse into a white dwarf of radius 3.5103km , what would its period be if no mass were ejected and a sphere of uniform density can model the Sun both before and after?
Given the perihelion distance, p , and aphelion distance, q , for an elliptical orbit, show that the velocity at perihelion, vp , is given by vp=2GMSun(q+p)qp . (Hint: Use conservation of angular momentum to relate vp and vq , and then substitute into the conservation fo energy equation.)
Circular orbits in Equation 13.10 for conic sections must have eccentricity zero. From this, and using Newton’s second law applied to centripeta acceleration, show that the value of in Equation 13.10 is given by Where is the angular momentum of the orbiting body. The value of is constant and given by this expression regardless of the type of orbit.
Using Figure 13.9, carefull sketch a free body diagram for the case of a simple pendulum hanging at latitude lambda, labeling all forces acting on the point mass,m. Set up the equations of motion for equilibrium, setting one coordinate in the direction of the centripetal accleration (toward P in the diagram), the other perpendicular to that. Show that the deflection angle , defined as the angle between the pendulum string and the radial direction toward the center of Earth, is given by the expression below. What is the deflection angle at latitude 45 degrees? Assume that Earth is a perfect sphere. tan(+)=gg2REtan , where is the angular velocity of Earth.
The mass of Earth is 5.971024kg and its orbital radius is an average of 1.501011m . Calculate the magnitude of its linear momentum at the location in the diagram.
Two stars of masses M and m, separated by a distance d, revolve in circular orbits about their center of mass (Fig. P11.50). Show that each star has a period given by T2=42d3G(M+m) Proceed as follows: Apply Newtons second law to each star. Note that the center-of-mass condition requires that Mr2 = mr1, where r1 + r2 = d.
Two planets X and Y travel counterclockwise in circular orbits about a star as shown in Figure P11.14. The radii of their orbits are in the ratio 3:1. At one moment, they are aligned as shown in Figure P11.14a, making a straight line with the star. During the next five years, the angular displacement of planet X is 90.0 as shown in Figure P11.14b. What is the angular displacement of planet Y at this moment?
Check Your Understanding Assume you are in a spacecraft in orbit about the Sun at Earth’s orbit, but far away from Earth (so that it can be ignored). How could you redirect your tangential velocity to the radial direction such that you could then pass by Mars’s orbit? What would be required to change just the direction of the velocity?
The angle between two radii of a circle with radius 1.50 m is 0.700 rad. What length of arc is intercepted on the circumference of the circle by the two radii?
Suppose a star the size of our Sun, but with mass 5.0 times as great, were rotating at a speed of 1.0 revolution every 10 days. If it were to undergo gravitational collapse to a neutron star of radius 14 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume also that the thrown- off mass carries off either. a) no angular momentum b) its proportional share three-quarters of the initial angular momentum
Answer without rounding off: (COLLAB Gauss's Law for Mass) Journey through the Center of the Earth. A 1024-kg blue ball is dropped from an initial z-position of 2.1 x 106 m through the center of a planet with a radius of 7.7 x 106 m. If the mass of the planet is 46.5 x 1015 kg, measure the displacement of the ball at time t = 6 s?