Ch 12: Rotation of a Rigid Body
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Problem 12
A thin, 100 g disk with a diameter of 8.0 cm rotates about an axis through its center with 0.15 J of kinetic energy. What is the speed of a point on the rim?Problem 12
A long, thin rod of mass M and length L is standing straight up on a table. Its lower end rotates on a frictionless pivot. A very slight push causes the rod to fall over. As it hits the table, what are (a) the angular velocityProblem 12
The three 200 g masses in FIGURE EX12.11 are connected by massless, rigid rods. (b) What is the triangle's kinetic energy if it rotates about the axis at 5.0 rev/s?
Problem 12
What is the rotational kinetic energy of the earth? Assume the earth is a uniform sphere. Data for the earth can be found inside the back cover of the book.Problem 12
A long, thin rod of mass M and length L is standing straight up on a table. Its lower end rotates on a frictionless pivot. A very slight push causes the rod to fall over. As it hits the table, what are (b) the speed of the tip of the rod?Problem 12
A 4.0-cm-diameter disk with a 3.0-cm-diameter hole rolls down a 50-cm-long, 20° ramp. What is its speed at the bottom? What percent is this of the speed of a particle sliding down a frictionless ramp?Problem 12
A solid sphere of radius R is placed at a height of 30 cm on a 15° slope. It is released and rolls, without slipping, to the bottom. From what height should a circular hoop of radius R be released on the same slope in order to equal the sphere's speed at the bottom?Problem 12
A 750 g disk and a 760 g ring, both 15 cm in diameter, are rolling along a horizontal surface at 1.5 m/s when they encounter a 15° slope. How far up the slope does each travel before rolling back down?Problem 12
A solid spherical marble shot up a frictionless 15° slope rolls 2.50 m to its highest point. If the marble is shot with the same speed up a slightly rough 15° slope, it rolls only 2.30 m. What is the coefficient of rolling friction on the second slope?Problem 12
A small 300 g ball and a small 600 g ball are connected by a 40-cm-long, 200 g rigid rod. a. How far is the center of mass from the 600 g ball?Problem 12
Two balls are connected by a 150-cm-long massless rod. The center of mass is 35 cm from a 75 g ball on one end. What is the mass attached to the other end?Problem 12
The four masses shown in FIGURE EX12.13 are connected by massless, rigid rods. (a) Find the coordinates of the center of mass.
Problem 12
The three masses shown in FIGURE EX12.15 are connected by massless, rigid rods.(a) Find the coordinates of the center of mass.
Problem 12
The three masses shown in FIGURE EX12.15 are connected by massless, rigid rods. (b) Find the moment of inertia about an axis that passes through mass A and is perpendicular to the page.
Problem 12
An object whose moment of inertia is 4.0 kg m^2 is rotating with angular velocity 0.25 rad/s. It then experiences the torque shown in FIGURE EX12.25. What is the object's angular velocity at t = 3.0s?
Problem 12
In FIGURE EX12.19, for what value of Xaxle will the two forces provide 1.8 Nm of torque about the axle?
Problem 12
Force F = ─10ĵ N is exerted on a particle at 𝓇 = (5î＋5ĵ) m. What is the torque on the particle about the origin?Problem 12
An 8.0-cm-diameter, 400 g solid sphere is released from rest at the top of a 2.1-m-long, 25 incline. It rolls, without slipping, to the bottom(b). What fraction of its kinetic energy is rotational?Problem 12
An object's moment of inertia is 2.0 kg m^2. Its angular velocity is increasing at the rate of 4.0 rad/s per second. What is the net torque on the object?Problem 12
A 1.0 kg ball and a 2.0 kg ball are connected by a 1.0-m-long rigid, massless rod. The rod is rotating cw about its center of mass at 20 rpm. What net torque will bring the balls to a halt in 5.0 s?Problem 12
A 12-cm-diameter, 600 g cylinder, initially at rest, rotates on an axle along its axis. A steady 0.50 N force applied tangent to the edge of the cylinder causes the cylinder to reach an angular velocity of 500 rpm in 2.0 s. What is the magnitude of the frictional torque between the cylinder and the axle?Problem 12
A 4.0-m-long, 500 kg steel beam extends horizontally from the point where it has been bolted to the framework of a new building under construction. A 70 kg construction worker stands at the far end of the beam. What is the magnitude of the torque about the bolt due to the worker and the weight of the beam?Problem 12
The object shown in FIGURE EX12.29 is in equilibrium. What are the magnitudes of F1 and F2
Problem 12
Vector A ＝ 3î＋ĵ and vector B＝ 3î ─ 2ĵ ＋ 2k. What is the cross product A ✕ B?Problem 12
Evaluate the cross products and A ✕ B and C ✕ D.
Problem 12
A small 300 g ball and a small 600 g ball are connected by a 40-cm-long, 200 g rigid rod. b. What is the rotational kinetic energy if the structure rotates about its center of mass at 100 rpm?Problem 12
Your task in a science contest is to stack four identical uniform bricks, each of length L, so that the top brick is as far to the right as possible without the stack falling over. Is it possible, as FIGURE P12.60 shows, to stack the bricks such that no part of the top brick is over the table? Answer this question by determining the maximum possible value of d.Problem 12
The four masses shown in FIGURE EX12.13 are connected by massless, rigid rods. (b) Find the moment of inertia about a diagonal axis that passes through masses B and D.Problem 12
A rod of length L and mass M has a nonuniform mass distribution. The linear mass density (mass per length) is λ = cx^2 , where x is measured from the center of the rod and c is a constant. c. Find an expression in terms of L and M for the moment of inertia of the rod for rotation about an axis through the center.Problem 12
A satellite follows the elliptical orbit shown in FIGURE P12.77. The only force on the satellite is the gravitational attraction of the planet. The satellite's speed at point 1 is 8000 m/s. a. Does the satellite experience any torque about the center of the planet? Explain.
