As shown in the figure, a homogeneous rod with a length L = 1 (m) and mass m 0.5 (kg) is fixed so that it can rotate in the middle. Two springs with constant k= 12 (N/m) are connected at both ends of the rod. The other ends of the springs are fixed and the springs are unstretched. The rod is rotated as 6 « from its equilibrium position and released. What is the angular frequency of the rod in (rad/s)? g = 10 (m/s³)

As shown in the figure, a homogeneous rod with a length L = 1 (m) and mass m 0.5 (kg) is fixed so that it can rotate in the middle. Two springs with constant k= 12 (N/m) are connected at both ends of the rod. The other ends of the springs are fixed and the springs are unstretched. The rod is rotated as 6 « from its equilibrium position and released. What is the angular frequency of the rod in (rad/s)? g = 10 (m/s³)

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter13: Rotation Ii: A Conservation Approach

Section: Chapter Questions

Problem 47PQ

See similar textbooks

Similar questions

A hoop of radius RH and mass mH and a solid cylinder of radius Rc and mass mc are released simultaneously at the top of a plane ramp of length L inclined at angle θ above horizontal. Which reaches the bottom first, and what is the speed of each there?
A uniform sphere of mass m and radius R rolls without slipping down a plane at an angle θ from thehorizontal. Show that the acceleration along the slope of the center of mass is aCM = (5/7)g sin θ and that the force of static friction needed is fs = (2/7)mg sin θ. What minimum coefcient of friction µs is needed to satisfythe conditions of the problem?
In the assembly below the system can rotate around the vertical axis. The left part is a square where R = 0.1 meters, and the mass of each of the four thin bars is uniform and is 0.1 kg. On the left is a massive sphere of radius R = 0.2 meters and Mass M = 0.3 kg. Assume that the system rotates with constant period T = 2.0 s, when, without any external action, as three leftmost bars detach from the system, leaving only the right vertical bar (on the axis) and sphere . What will be the new period of system revolution? Note: Note that in this case there is no difference between angular velocity and frequency.
A simple pendulum consists of a 0.8-kg bob connected to a massless inextensible cord with a length L = 1.4 m. The bob is set into motion and its angular displacement is given by e(t) = 0.11cos(wt), where is in radians and tis in seconds. Take g = 9.8 m/s^2, determine the mechanical energy of this pendulum.
a solid brass ball of mass 0.280 g will roll smoothly along a loop-the-loop track when released from rest along the straight section. The circular loop has radius R = 14.0 cm, and the ball has radius r < R. (a) What is h if the ball is on the verge of leaving the track when it reaches the top of the loop? If the ball is released at height h = 6.00R, what are the (b) magnitude and (c) direction of the horizontal force component acting on the ball at point Q?
You pull on a string with a horizontal force of magnitude Fyb = 44 N that is attached to a block of mass mb = 6.1 kg, then to the axle of a solid cylinder of mass mc = 4.7 kg and radius r = 0.4 m, then to a spring of spring constant k = 135 N/m. This is all done on an inclined plane where there is friction ( μs = 0.61 and μk = 0.34 ), and the incline angle is θ = 30 degrees. Everything starts at rest, and the spring is unstretched. The block slides down the plane, the cylinder rolls down the plane (without slipping), and the spring stretches. First, what is the speed of the block and cylinder after you have pulled the block and cylinder 107 cm down the plane? How far have you pulled the block and cylinder when everything stops? I can not figure out this homework question.
You pull on a string with a horizontal force of magnitude Fyb = 44 N that is attached to a block of mass mb = 6.1 kg, then to the axle of a solid cylinder of mass mc = 4.7 kg and radius r = 0.4 m, then to a spring of spring constant k = 135 N/m. This is all done on an inclined plane where there is friction ( μs = 0.61 and μk = 0.34 ), and the incline angle is θ = 30 degrees. Everything starts at rest, and the spring is unstretched. The block slides down the plane, the cylinder rolls down the plane (without slipping), and the spring stretches. How far have you pulled the block and cylinder when everything stops? The velocity when it has traveled 44 cm down the plane is 2.030 m/s.
Calculate the m.і. of a thin uniform rod of the mass 100g and length 60cm about an axis perpendicular to its length and passing through (1) its centre and (2) one end.
A small ball of mass 0.5 kg is attached to one end of a 1.8-m-long massless rod, and the other end of the rod is hung from a pivot. When the resulting pendulum is 40◦ from the vertical, what is the magnitude of thegravitational torque calculated about the pivot?
How much torque must be applied to a 6.0 kg flywheel with a diameter of 30 cm, that is in a shape of a solid circular plate, to change its frequency from 1000 min-1 to 2500 min-1?
You pull on a string with a horizontal force of magnitude Fyb = 47 N that is attached to a block of mass mb = 7.9 kg, then to the axle of a solid cylinder of mass mc = 4.4 kg and radius r = 0.4 m, then to a spring of spring constant k = 200 N/m. This is all done on an inclined plane where there is friction ( μs = 0.65 and μk = 0.37 ), and the incline angle is θ = 26 degrees. Everything starts at rest, and the spring is unstretched. The block slides down the plane, the cylinder rolls down the plane (without slipping), and the spring stretches. First, what is the speed of the block and cylinder after you have pulled the block and cylinder 27 cm down the plane?
You pull on a string with a horizontal force of magnitude Fyb = 32 N that is attached to a block of mass mb = 6.5 kg, then to the axle of a solid cylinder of mass mc = 4.0 kg and radius r = 0.4 m, then to a spring of spring constant k = 185 N/m. This is all done on an inclined plane where there is friction ( μs = 0.69 and μk = 0.40 ), and the incline angle is θ = 28 degrees. Everything starts at rest, and the spring is unstretched. The block slides down the plane, the cylinder rolls down the plane (without slipping), and the spring stretches. First, what is the speed of the block and cylinder after you have pulled the block and cylinder 6 cm down the plane? How far have you pulled the block and cylinder when everything stops?