Q. A uniform hemisphere of mass m = 5 kg. and radius r = 0.5m. is released from rest on a horizontal surface in the position when OG is horizontal as shown in the figure below. The mass centre G of the hemisphere is at a distance (3/8)r from point O and its mass moment of inertia about O is I = (2/5)mr². If the friction between the hemisphere and the horizontal surface is sufficient to prevent slipping, (3/8)r G (b) set up a global reference axes system of your choice, and draw the free body, kinematic and kinetic diagrams for the hemisphere showing all the forces and moments acting on it at the initiation of its motion, (c) write down the relevant kinetic and kinematic relationships with respect to the reference axes system, and (d) determine the angular acceleration a of the hemisphere and the frictional force F and the normal force N at the contact point.

Q. A uniform hemisphere of mass m = 5 kg. and radius r = 0.5m. is released from rest on a horizontal surface in the position when OG is horizontal as shown in the figure below. The mass centre G of the hemisphere is at a distance (3/8)r from point O and its mass moment of inertia about O is I = (2/5)mr². If the friction between the hemisphere and the horizontal surface is sufficient to prevent slipping, (3/8)r G (b) set up a global reference axes system of your choice, and draw the free body, kinematic and kinetic diagrams for the hemisphere showing all the forces and moments acting on it at the initiation of its motion, (c) write down the relevant kinetic and kinematic relationships with respect to the reference axes system, and (d) determine the angular acceleration a of the hemisphere and the frictional force F and the normal force N at the contact point.

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter7: Dry Friction

Section: Chapter Questions

Problem 7.26P: The uniform plank is initially at rest on the fixed support at A and the stationary drum at B. If...

See similar textbooks

Similar questions

The centroidal mass moment of inertia ofthe pulley assembly is 20 ft-lb-s2. Determine (a) the tension in the cordsupporting 161-lb block , (b)the tension supporting the 322-lb block, and (c) the angularacceleration of the pulley system .Hint: Determine first the direction ofmotion, i.e. will block A move up ordown?
cable is wrapped around the spool’s center hub. The mass of the spool is m= 100 kg, the radius r1 = 0.4 m, r2 =0.6 m, and the radius of gyration is kG = 0.3 m. A horizontal force P = 10 N is applied to the cord. The spool is initially at rest and rolls without slipping. (2) The mass moment of inertia of the spool about point A _______(kg·m2)(two decimal places)
The pendulum shown in the image below can rotate about the axisperpendicular to page and pass through point O. The solid rod hasa mass m=6 kg and the solid sphere diameter of 50 mm has a massof 1.5m(kg). Calculate the mass moment of inertia of the rod andthe sphere at 0° when the axis is perpendicular to the page andpass through the centre of gravity. (l= 800 mm; k= 600 mm)
A uniform hemisphere of mass m = 5 kg. and radius r = 0.5m. is released from rest on a horizontal surface in the position when OG is horizontal as shown in the figure below. The mass centre G of the hemisphere is at a distance (3/8)r from point O and its mass moment of inertia about O is ( ) 2 1 0 = 2/ 5 mr . If the friction between the hemisphere and the horizontal surface is sufficient to prevent slipping, (3/8)r Hand draw the free body, kinematic and kinetic diagrams for the hemisphere (shown above) showing all the forces and moments acting on it at the initiation of its motion
The 285-kg wheel has a radius of gyration about its center O of ko = 300 mm, and radius r = 0.4 m. When the wheel is subjected to the constant couple moment M = 74 N•m, it starts rolling from rest. Determine the mass moment of inertia //c (in kg. m²) about the wheel's /C. Please pay attention: the numbers may change since they are randomized. Your answer must include 1 place after the decimal point. Take g = 9.81 m/s². M Your Answer: Answer
2 An object is made of two identical uniform 3m long rods connected as shown. The total mass of the system is 60kg. The object can rotate in the plane of the page about a fixed axis at Point A. There is a friction moment of 500 N m about point A. a. What is the mass moment of inertia of the object about Point A? b. If the object is released from rest in the orientation shown, what will be is initial angular acceleration? stationary Mf A = total mass= 60 kg 500 Nm 3 m 3 m g
Can anyone help me with this question
At the instant shown, the uniform slender rod with mass m = 33 kg is pin-supported at point O. It has dimensions a = 0.22 m and b = 0.49 m. Determine its mass moment of inertia / (in kg.m²) about the axis that passes point O and is perpendicular to the screen. Please pay attention: the numbers may change since they are randomized. Your answer must include 3 places after the decimal point. a Your Answer: Answer M b
A car is moving on a curved horizontal road of radius 100 m with a speed of 20 m/s. The rotating masses of the engine have an angular speed of 100 rad/s in clockwise direction when viewed from the front of the car The combined moment of inertia of the rotating masses is 10 kg-m².what is the magnitude of the gyroscopic moment in (N-m)?
Include FBD
4. Draw the FBD and derive the EOM of the pulley system below with respect to x using Newton's laws. Mass m slides on a rough surface with friction force f. There is no displacement in the spring initially. -Pulley. moment of inertia J,
At the instant shown, the uniform slender rod with mass m = 32 kg is pin-supported at point O. It has dimensions a = 0.24 m and b = 0.70 m. Determine its mass moment of inertia lo (in kg•m2) about the axis that passes point O and is perpendicular to the screen. Please pay attention: the numbers may change since they are randomized. Your answer must include 3 places after the decimal point. a b M Your Answer: Answer