In order to find the radius of gyration of a car, it is suspended with its axis vertical from three parallel wires 2.5 metres long. The wires are attached to the rim at points spaced 120° apart and at equal distances 250 mm from the axis. It is found that the wheel makes 50 torsional oscillations of small amplitude about its axis in 170 seconds. Find the radius of gyration of the wheel.

Question

In order to find the radius of gyration of a car, it is suspended with its axis vertical from three parallel wires 2.5 metres long. The wires are attached to the rim at points spaced 120° apart and at equal distances 250 mm from the axis. It is found that the wheel makes 50 torsional oscillations of small amplitude about its axis in 170 seconds. Find the radius of gyration of the wheel.

asked Sep 24, 2022 in Machine Kinematics by Leo (38.0k points)

In order to find the radius of gyration of a car, it is suspended with its axis vertical from three parallel wires 2.5 metres long. The wires are attached to the rim at points spaced 120° apart and at equal distances 250 mm from the axis. It is found that the wheel makes 50 torsional oscillations of small amplitude about its axis in 170 seconds. Find the radius of gyration of the wheel.

(a) 168 mm

(b) 268 mm

(c) 368 mm

(d) 468 mm

I have been asked this question during an online exam.

I would like to ask this question from Closely-coiled Helical Spring and Compound Pendulum topic in chapter Simple Harmonic Motion of Machine Kinematics

1 Answer

Related questions

+1 vote

1 answer

A small connecting rod of mass 1.5 kg is suspended in a horizontal plane by two wires 1.25 m long. The wires are attached to the rod at points 120 mm on either side of the centre of gravity. If the rod makes 20 oscillations in 40 seconds, find the radius of gyration of the rod about a vertical axis through the centre of gravity.

asked Sep 24, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

A connecting rod of mass 5.5 kg is placed on a horizontal platform whose mass is 1.5 kg. It is suspended by three equal wires, each 1.25 m long, from a rigid support. The wires are equally spaced round the circumference of a circle of 125 mm radius. When the c.g. of the connecting rod coincides with the axis of the circle, the platform makes 10 angular oscillations in 30 seconds. Determine the mass moment of inertia about an axis through its c.g.

asked Sep 24, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

A small connecting rod of mass 1.5 kg is suspended in a horizontal plane by two wires 1.25 m long. The wires are attached to the rod at points 120 mm on either side of the centre of gravity. If the rod makes 20 oscillations in 40 seconds, find the mass moment of inertia of the rod about a vertical axis through the centre of gravity.

asked Sep 24, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

A horizontal bar 1.5 metres long and of small cross-section rotates about vertical axis through one end. It accelerates uniformly from 1200 r.p.m. to 1500 r.p.m. in an interval of 5 seconds. What is the linear velocity at the beginning of the interval ?

asked Sep 23, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

A horizontal bar 1.5 metres long and of small cross-section rotates about vertical axis through one end. It accelerates uniformly from 1200 r.p.m. to 1500 r.p.m. in an interval of 5 seconds. What is the linear velocity at the beginning?

asked Sep 23, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

A horizontal bar 1.5 metres long and of small cross-section rotates about vertical axis through one end. It accelerates uniformly from 1200 r.p.m. to 1500 r.p.m. in an interval of 5 seconds. What is the linear velocity at the end of the interval ?

asked Sep 23, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

A horizontal bar 1.5 metres long and of small cross-section rotates about vertical axis through one end. It accelerates uniformly from 1200 r.p.m. to 1500 r.p.m. in an interval of 5 seconds. What is the normal component of the acceleration of the mid-point of the bar after 5 seconds after the acceleration begins ?

asked Sep 24, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

A horizontal bar 1.5 metres long and of small cross-section rotates about vertical axis through one end. It accelerates uniformly from 1200 r.p.m. to 1500 r.p.m. in an interval of 5 seconds. What is the tangential component of the acceleration of the mid-point of the bar after 5 seconds after the acceleration begins ?

asked Sep 23, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

A particle executes linear simple harmonic motion with an amplitude of 2 cm. When the particle is at 1 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is

asked Sep 23, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

A haulage rope winds on a drum of radius 500 mm, the free end being attached to a truck. The truck has a mass of 500 kg and is initially at rest. The drum is equivalent to a mass of 1250 kg with radius of gyration 450 mm. The rim speed of the drum is 0.75 m/s before the rope tightens. By considering the change in linear momentum of the truck and in the angular momentum of the drum, find the speed of the truck when the motion becomes steady.

asked Sep 24, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

A flywheel is mounted on a vertical shaft. The both ends of a shaft are fixed and its diameter is 50 mm. The flywheel has a mass of 500 kg, the modulus of rigidity for the shaft material is 80 GN/m^2 and its radius of gyration is 0.5 m. Find the natural frequency of torsional vibrations.

asked Sep 22, 2022 in Machine Dynamics by Grayson (34.3k points)

+1 vote

1 answer

Two concentric springs with stiffness equal to 100 N/mm and 80 N/mm respectively, when subjected to a load of 900 N will deflect by

asked Sep 24, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

A helical spring, of negligible mass, and which is found to extend 0.25 mm under a mass of 1.5 kg, is made to support a mass of 60 kg. The spring and the mass system is displaced vertically through 12.5 mm and released. Find the velocity of the mass, when it is 5 mm below its rest position.

asked Sep 24, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

The periodic time of a compound pendulum is …….. when the distance between the point of suspension and the center of gravity is equal to the radius of gyration of the body about its center of gravity.

asked Sep 24, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

When a rigid body is suspended vertically and it oscillates with a small amplitude under the action of the force of gravity, the body is known as

asked Sep 24, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

The piston of an engine moves with SIMPLE HARMONIC MOTION. The crank rotates at a speed of 120 r.p.m. with a stroke of 2 metres. Find the velocity of the piston in m/s, when it is at a distance of 0.75 metre from the centre.

asked Sep 24, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

The piston of an engine moves with SIMPLE HARMONIC MOTION. The crank rotates at a speed of 120 r.p.m. with a stroke of 2 metres. Find the velocity of the piston in m/s^2, when it is at a distance of 0.75 metre from the centre.

asked Sep 24, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

If a simple pendulum oscillates with an amplitude 50 mm and time period 2s, then its maximum velocity is

asked Sep 24, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

The piston of a steam engine moves with simple harmonic motion. The crank rotates at 120 r.p.m. with a stroke of 2 metres. Find the velocity of the piston, when it is at a distance of 0.75 metre from the centre.

asked Sep 24, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

The piston of a steam engine moves with simple harmonic motion. The crank rotates at 120 r.p.m. with a stroke of 2 metres. Find the acceleration of the piston, when it is at a distance of 0.75 metre from the centre.

asked Sep 24, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

If the radius of gyration of a compound pendulum about an axis through c.g. is more, then its frequency of oscillation will be

asked Sep 23, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

A rigid body has a radius of gyration of 20cm, if its moment of inertia is 10 Kg-m^2, find its mass in kilograms.

asked Sep 24, 2022 in Machine Kinematics by Leo (38.0k points)

+1 vote

1 answer

An aeroplane makes a complete half circle of 50 metres radius, towards left, when flying at 200 km per hr. The rotary engine and the propeller of the plane has a mass of 400 kg and a radius of gyration of 0.3 m. The engine rotates at 2400 r.p.m. clockwise when viewed from the rear. Find the gyroscopic couple on the aircraft.

asked Sep 22, 2022 in Machine Dynamics by Grayson (34.3k points)

+1 vote

1 answer

While turning a 4-wheel tractor equipped with the Ackermann steering mechanism the axis of the inner front wheel makes an angle of 45°, whereas the angle made by the axis of the outer front wheel is 30° with horizontal line parallel to the front axle. The kingpins of the axle are 1300 mm apart. The spindle genths are essentially zero. What should be the wheel base of the tractor if there is no slippage of any of the wheels?

asked Jan 29, 2022 in Farm Machinery by Olivia (38.9k points)

+1 vote

1 answer

A point moves with SIMPLE HARMONIC MOTION. When this point is 0.75 m away from the mid path, it has a velocity of 11 m/s and when 2 m from the centre of its path its velocity is 3 m/s. Find its angular velocity in rad/s.

asked Sep 24, 2022 in Machine Kinematics by Leo (38.0k points)

Greg · Answer 1 · 2022-10-17T22:24:37+0000

Correct option is (b) 268 mm

Explanation: Given : l = 2.5 m ; r = 250 mm = 0.25 m ;

Since the wheel makes 50 torsional oscillations in 170 seconds, therefore frequency of oscillation,

n = 50/170 = 5/17 Hz

Let kG = Radius of gyration of the wheel

We know that frequency of oscillation (n),

5/17 = r/2πkG √g/l = 0.25/2πkG√9.81/2.5 = 0.079/kG

kG = 0.079 x 17/5 = 0.268 m = 268 mm.

Please log in or register to answer this question.

1 Answer

Please log in or register to add a comment.

Related questions

Categories