1. What conditions must be present for (a) translational equilibrium and (b) rotational equilibrium of a rigid body? 2. If these conditions for equilibrium are satisfied, is the rigid body necessarily in static equilibrium? Explain. 3. What are the general definition and mathematical expression for torque?
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- 6. A yoyo is dropped as shown in the figure below. Neglect air friction. The mass of the yoyo is 0.160 kg, R = 10 cm and Ro = 2.0 cm. a. Show and label the translational forces acting on the yo-yo's center of gravity. Show and label the force(s) exerting non- zero torque(s) about the yo-yo's center of gravity at their point of application. Only show non-zero torques. b. If the linear acceleration of the yo-yo is 2.0 m/s/s, determine the tension of the string.How to solve number 12. Let F = 4 i -6 j + 2 k and Let r = 3 i -3 j - 5 k. Find the torque in both Cartesian and polar coordinates. (Find Torque by cross product, find the magnitude of the torque, find the SOLID angle theta and phi since the vector will be in 3 dimensions.) ____________________________________________________________________________________________________________________________________________________________________________ If you could clearly circle the answer I need, that would be great! Thanks!
- 2. Let F = 4 i -6 j+ 2 k and Let r = 3 i -3 j - 5 k. Find the torque in both %3D Cartesian and polar coordinates. (Find Torque by cross product, find the magnitude of the torque, find the SOLID angle theta and phi since the vector will be in 3 dimentsions.).4. Three forces are acting on a rectangular block of wood as shown, with a pivot in the lower-left corner. a. Find the torque on the block due to each force. Use the convention where a counterclockwise torque is positive. ΤΑ TB = = TC = + 0.5m pivot 0.2m с A B 30N 20N 10N1. Perform analysis steps B.1. Derive an algebraic equation for the moment of inertia of the disk/plate by using the conservation of energy method. The variables in your equations should be the values you can measure (e.g., mass of hanger, angular velocities, angular acceleration, positions and/or velocities of the falling mass, etc.) and physical constants (i.e., the acceleration due to gravity). You should do this on a separate sheet and keep a copy as you will need it during the lab.
- 1. A point on the outer rim of a hollow disk (I = mr2) with radius r and mass m rotates with a constant angular speed of ω. How far will the point travel (in meters) in 1 minute of rotation? Let w=11.5 rad/s and r=0.78m a. how many revolutions will the point experience during this time? b. What net torque is necessary to stop the disk in time t? Let t=7 sec and m =14kg1. Calculate the torque about the z-axis pointing out of the page at the origin in the following - figure given that F₁ =3 N, F₂ = 9 N, F3=8 N, F₁=2 N. Hint: Use the sign convention for torques, counter-clockwise rotation corresponds to a torque in the positive z-direction and clockwise rotation corresponds to a torque in the negative z-direction. Which forces produce clockwise rotations and which forces produce counter-clockwise rotations? While using the formula for cross-product A x B= ABsine, remember that is the angle between the tails of the vectors A and B. To determine 0 rearrange the vectors so that their tails coincide. Nm k net = F₂ 30° F3 YA 2 m O 3 m 2 m F4 20° F₁3. Consider two thin-walled beams of the same wall thickness with cross- sections as shown in Figure 2. Applied torque is the same for both beams. Beams are twisted such that twisting angles are equal to each other. Find the relation between R2 and R₁ for the case = π/3. What will be this relation if we double the center angle o? R₁ R₁ R₂ FIGURE 2. Cross-sections of two thin-walled beams.