Question

In: Physics

The thin uniform rod in the figure has length 5.0 m and can pivot about a...

The thin uniform rod in the figure has length 5.0 m and can pivot about a horizontal, frictionless pin through one end. It is released from rest at angle θ = 50° above the horizontal. Use the principle of conservation of energy to determine the angular speed of the rod as it passes through the horizontal position. Assume free-fall acceleration to be equal to 9.83 m/s2.

Expert Solution

mechanical energy at point A is only potential

where:
It is the acceleration of gravity
It is the mass of the bar

It is the height of the center of mass and is calculated as follows

mechanical energy at point B is only rotational kinetic, is given by:

where

moment of inertia A rod with respect to an end

angular velocity

as the mechanical energy is constant

replacing

simplifying m

expression for the angular velocity

evaluated numerically

genius_generous answered 9 months ago

The figure is an overhead view of a thin uniform rod of length 0.467 m and...

The figure is an overhead view of a thin uniform rod of length 0.467 m and mass M rotating horizontally at angular speed 15.7 rad/s about an axis through its center. A particle of mass M/3 initially attached to one end is ejected from the rod and travels along a path that is perpendicular to the rod at the instant of ejection. If the particle's speed vp is 3.32 m/s greater than the speed of the rod end just after...

QUESTION 1: A thin uniform rod has a length of 0.400 m and is rotating in...

QUESTION 1: A thin uniform rod has a length of 0.400 m and is rotating in a circle on a frictionless table. The axis of rotation is perpendicular to the length of the rod at one end and is stationary. The rod has an angular velocity of 0.35 rad/s and a moment of inertia about the axis of 2.90×10−3 kg⋅m2 . A bug initially standing on the rod at the axis of rotation decides to crawl out to the other...

A uniform thin rod of length 0.4 m and mass 0.5 kg can rotate in a...

A uniform thin rod of length 0.4 m and mass 0.5 kg can rotate in a horizontal plane about a vertical axis on the left end of the rod. The rod is at rest when a 10.0-g bullet traveling in the horizontal plane of the rod is fired into the right end of the rod at an angle 90o with the rod. The bullet lodges in the rod and the angular velocity of the rod is 10 rad/s immediately after...

A 5.0 kg rod with a length of 2.8 m has an axis of rotation at...

A 5.0 kg rod with a length of 2.8 m has an axis of rotation at its center. Looking at the rod with its axis perpendicular to this page, a force of 14.5 N at 68o is applied to the rod 1.1 m from the axis of rotation. This torque would angularly accelerate the rod in a counter-clockwise direction. Assume that the torque continues to be applied during the motion consider in this problem and that there are no other...

A uniform thin rod of length 0.812 m is hung from a horizontal nail passing through...

A uniform thin rod of length 0.812 m is hung from a horizontal nail passing through a small hole in the rod located 0.043 m from the rod\'s end. When the rod is set swinging about the nail at small amplitude, what is the period of oscillation?

A uniform thin rod of length 0.778 m is hung from a horizontal nail passing through...

A uniform thin rod of length 0.778 m is hung from a horizontal nail passing through a small hole in the rod located 0.057 m from the rod's end. When the rod is set swinging about the nail at small amplitude, what is the period of oscillation?

Two identical uniform solid spheres are attached by a solid uniform thin rod, as shown in the figure.

Two identical uniform solid spheres are attached by a solid uniform thin rod, as shown in the figure. The rod lies on a line connecting the centers of mass of the two spheres. The axes A, B, C, and D are in the plane of the page (which also contains the centers of mass of the spheres and the rod), while axes E and F (represented by black dots) are perpendicular to the page. (Figure 1).Rank the moments of inertia...

A uniform rod of mass 2.20 kg and length 2.00 m is capable ofrotating about...

A uniform rod of mass 2.20 kg and length 2.00 m is capable of rotating about an axis passing through its center and perpendicular to its length. A mass m1 = 4.90 kg is attached to one end and a second mass m2 = 2.60 kg is attached to the other end of the rod. Treat the two masses as point particles. At the origina of an xy-coordinate plane a rod of length labeled l rotates around it's midpoint. Attached to...

A thin copper rod has a mass per unit length of 0.1 kg/m. What is the...

A thin copper rod has a mass per unit length of 0.1 kg/m. What is the minimum current in the rod that would allow it to levitate above the ground in a magnetic field of magnitude 0.5 T? (g = 10.0 m/s2) 2.9 A 2.5 A 2.2 A 2.0 A 1.8 A

In the figure, a uniform plank, with a length L of 5.23 m and a weight...

In the figure, a uniform plank, with a length L of 5.23 m and a weight of 280 N, rests on the ground and against a frictionless roller at the top of a wall of height h = 1.59 m. The plank remains in equilibrium for any value of θ = 70.0° or more, but slips if θ < 70.0°. Find the coefficient of static friction between the plank and the ground.