The particle of mass m = 2.4 kg is attached to the light rigid rod of length L = 0.77 m, and the assembly rotates about a horizontal axis through O with a constant angular velocity θ˙θ˙ = ω = 3.5 rad/s. Determine the force T in the rod when θ = 29°. The force T is positive if in tension, negative if in compression.
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The particle of mass m = 2.4 kg is attached to the light rigid rod of length L = 0.77 m, and the assembly rotates about a horizontal axis through O with a constant
![Part 1
Answers:
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Calculate the r- and 8-components of acceleration.
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- A uniform wheel of mass 10.0 kg and radius 0.400 m is mounted rigidly on an axle through its center (see the figure). The radius of the axle is 0.200 m, and the rotational inertia of the wheel-axle combination about its central axis is 0.600 kg·m2. The wheel is initially at rest at the top of a surface that is inclined at angle θ = 67.2o with the horizontal; the axle rests on the surface while the wheel extends into a groove in the surface without touching the surface. Once released, the axle rolls down along the surface smoothly and without slipping. When the wheel-axle combination has moved down the surface by 9.29 m, what are (a) its rotational kinetic energy and (b) its translational kinetic energy?A uniform spherical shell of mass M = 15.0 kg and radius R = 0.600 m can rotate about a vertical axis on frictionless bearings (see the figure). A massless cord passes around the equator of the shell, over a pulley of rotational inertia / = 0.0560 kg-m2 and radius r = 0.0520 %3D m, and is attached to a small object of mass m = 4.20 kg. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object when it has fallen a distance 0.732 m after being released from rest? Use energy considerations. М, R Number i UnitsA thin spherical shell has a radius of 1.90 m. An applied torque of 960 Nm gives the shell an angular acceleration of 6.20 rad/s2 about an axis through the center of the shell.What are (a) the rotational inertia of the shell about that axis and (b) the mass of the shell?
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- A uniform thin rod of mass m = 3.2 kg and length L = 1.7 m can rotate about an axle through its center. Four forces are acting on it as shown in the figure. Their magnitudes are F1 = 3.5 N, F2 = 4.5 N, F3 = 15 N and F4 = 17 N. F2 acts a distance d = 0.21 m from the center of mass.Calculate the magnitude τ1 of the torque due to force F1, in newton meters. τ1 = Calculate the magnitude τ2 of the torque due to force F2 in newton meters. τ2 = Calculate the magnitude τ3 of the torque due to force F3 in newton meters. τ3 = Calculate the magnitude τ4 of the torque due to force F4 in newton meters. τ4 =Calculate the angular acceleration α of the thin rod about its center of mass in radians per square second. Let the counter-clockwise direction be positive. α =A uniform stick of mass M=2.98kg and length L=1.5m which is suspended horizontally with end B at the edge of a table and the other end A is held by hand. Point A is suddenly released. At the instant after release, what is the vertical acceleration of the center of mass. (Take g =9.81 m/s', for a uniform rod of mass M and length L the center of mass rotational inertia I,od = 1/12 ML2). Express your answer using one decimal place. m MA rod is laying on top on two poles. The rod is uniform and has a length of 3.22 m. The left pole is at the left end of the rod and the right pole is a 0.41m (d-0.41m) from the right side of the rod. What is the ratio of the forces F/FR on the rod due to the two poles?
- A beam, uniform in mass, M = 21 kg and length L = 24 m, hangs by a cable supported at point B, and rotates without friction around point A. On the end far of the beam, an object of mass m = 6 kg is hanging. The beam is making an angle of θ = 25° at point A with respect to the + x-axis. The cable makes an angle φ = 29° with respect to the - x-axis at B. Assume ψ = θ + φ. What is the horizontal force Sx the wall exerts on the beam at point A in terms of the tension T? What is the vertical force Sy that the wall exerts on the beam at point A in terms of the tension T, given parameters, and variables available in the palette?A uniform, solid sphere of radius 4.00 cm and mass 4.50 kg starts with a purely translational speed of 2.50 m/s at the top of an inclined plane. The surface of the incline is 2.75 m long, and is tilted at an angle of 34.0° with respect to the horizontal. Assuming the sphere rolls without slipping down the incline, calculate the sphere's final translational speed vz at the bottom of the ramp. U2 = m/sAn engineer estimates that under the most adverse expected weather conditions, the total force on the highway sign in the figure (Figure 1) will be F→=(±2.1i^−4.2j^)kN, acting at the cm. What is the magnitude of the torque this force exert about the base O? Express your answer using two significant figures.