A string is wound around a wheel while its free end is tied to the ceiling, as shown below. The wheel is released from rest so that it starts to rotate and moves downwards. The wheel has mass, m = 2.0 kg, radius r = 30 cm and moment of inertia 0.10 kgm? about the axis of rotation. string wheel Determine : (a) the linear acceleration of the wheel (b) the tension in the string

A string is wound around a wheel while its free end is tied to the ceiling, as shown below. The wheel is released from rest so that it starts to rotate and moves downwards. The wheel has mass, m = 2.0 kg, radius r = 30 cm and moment of inertia 0.10 kgm? about the axis of rotation. string wheel Determine : (a) the linear acceleration of the wheel (b) the tension in the string

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

4 -(Kinetics of Curvilinear Motion) Tow weights W, and W2 of 8KN and 5KN are attached at the ends of a flexible cable. The cable passes over a pulley of 100 cm diameter. The weight of the pulley is 600N with a radius of gyration of 50cm about its axis of rotation. Find the torque which must be applied to the pulley to raise the 8KN weight with an acceleration 1.5 m/s?. Neglect friction in the pulley bearing. 50 cm 600N T 8kN 5kN W,
Consider a hollow clay cylinder, which has a moment of inertia 55 kg-m2. The cylinder is free to rotate frictionless-ly, and it starts from rest. It rotate about a fixed axis through its center. Let's assume that we apply a tangential force to the end of the cylinder (the flat face of the shape) with a magnitude which can range 'from F = 0 to F = 75 N. The force can be applied at any distance from the axis of the cylinder ranging from R=0 to R=10 m from the axis of rotation. (a) Find a pair of values of F and R that cause the disk to complete 2.00 rev in 10.0 s. (b) Is your answer for the previos part unique? How many answers exist?
R - m 130° A hollow wheel of mass given by m 50 kg rolls down an incline of 30° without slipping. The inner radius of the wheel is given by R = 50 mm and its thickness is given by d = 5 mm. Gravity acts down. (a) Show that the moment of inertia of the wheel is given by Ī = 138 125 kg mm². (b) Show that the linear acceleration of the wheel's centre of gravity ā is related to the angular acceleration of the wheel a via a (55 mm)a. = (c) Analyse an appropriate free-body diagram to determine the linear acceleration of the wheel's centre of gravity ā.
A homogeneous beam AB weighs P, where a point is a rope wound around a homogeneous cylinder. The cylinder has radius R, mass m, and center of mass C is moving down the plumb line. Find 1) the acceleration of the circular wheel; 2) tension of rope; 3) Reaction force of bearing A and B H 112 12
A solid bar of mass m and length L stands vertically on a frictionless table and is then released to fall down. The moment of inertia about the center of mass is Ic = mL²/12. At the moment when the top end B just reaches the ground (0-0), (a) what are the angular velocity and angular acceleration? (b) what is the center-of-mass acceleration? (c) what is the normal force of the ground to end D? Hint: It may be helpful to find out the instant rotation axis. В m. L D
A string holds and wraps around a solid cylinder (7-kg and R = 8-m). A person pulls the string vertically upward, so the cylinder's center of gravity does not move and is suspended in midair for 7 second. Note that the rotational inertia of the cylinder about its axis is MR2/2, the tension in the string is 8- N. what is the net force on the cylinder in Newton? Note: Do not include the unit in your answer. T
A sphere of mass M and radius R is not necessarily solid or hollow. It has moment of inertia I= cMR2. As shown in the figure, the sphere starts from rest and rolls without slipping down a ramp from height H. It then moves back up the other side, but now with no friction at all between the sphere and the ramp. What height does the sphere reach?
A 40-kg disk shown is pin supported at its center. It starts from the rest and rotates to attain an angular velocity of 2 rad/s. The disk is acted upon by a constant couple moment M = 10 N.m clockwise. The spring is originally unstretched and its cord wraps around the rim of the disk. 0.2m ww Ol = a) (10 points) Find the kinetic energy of the disk. b) (30 points) Determine the angle through which the disk rotates
-. Solid disc with radius R=5 cm and mass M-4,5 kg is hanging on the ceiling. There is a rope wound around the disc. The rope is conducted through an ideal travelling pulley, and the end of the rope is fastened to the ceiling. The mentioned pulley carries a block with mass m=1kg. Find (a) the vertical translational acceleration of the block, (b) K=? force in the rope, (c) F=? force, which holds the disc on the ceiling. K ´R M m
A solid disc with radius R is connected to spring at point (d) distance above the center of disc. The other end of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the ground. The mass of disc is (M) and the spring constant is (K). The polar moment of inertia for disc about its center is J = 1/2MR2 , so the natural frequancy for the system is 1 2K(R+d)² MR2 the Answer is O 1 2K 2п 3M
A shaft caries four rotating masses A, B, C and D which are completely balanced. The masses B, C and Dare 50kg, 80kg and 70kg respectively. The masses C and D make angles of 90° and 195° respectively with mass B in the same sense. The masses A, B, C and D are concentrated at radius 75mm,100mm,50mm and 90mmrespectively.The plane of rotation of masses B and C are 250mm apart. Determine the magnitude of mass A and its angular position the position of planes A and D.
A machine part has the shape of a solid uniform sphere of mass 220 gg and diameter 3.50 cmcm . It is spinning about a frictionless axle through its center, but at a point at the top of the sphere, it is scraping against metal, resulting in a friction force of 0.0200 NN at that point. Find the angular acceleration of the sphere, including the direction (a positive value would indicate the +z direction and a negative value would indicate the -z direction).