A hoop and a cylinder of equal mass and radius roll down an inclined plane. Which one accelerates faster? Calculate the acceleration of the center-of-mass of each when rolling down a plane inclined at 15°.
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A hoop and a cylinder of equal mass and radius roll down an inclined plane. Which one accelerates faster? Calculate the acceleration of the center-of-mass of each when rolling down a plane inclined at 15°.
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- Take an equilateral triangular sheet of side, and remove the "middle" triangle (1/4 of the area). Then remove the "middle" triangle from each of the remaining three triangles, and so on, forever. Let the final object have mass. The moment of inertia of final object about axis passing through 'O' and perpendicular to plane of object is ml²/x. Then the value of x is5) In ice figure skating, a couple execute a “top” (see picture). The centre of mass of the woman (58 kg) is situated 1.3 m from the axis of rotation which is vertical and passes through the centre of mass of the man (85 kg). They are spinning at a constant angular velocity equal to ?? rad/s and the man and woman have moments of inertia, about their own centres of mass, equal to 1.6 and 2.5 kg.m2 respectively. Then the woman grabs the neck of the man. At this point, her moment of inertia decreases to 1.4 kg.m2 and her body centre of gravity is 0.9 m from the axis of rotation. Determine the new angular velocity. Hints: This is a conservation of angular momentum problem, and needs the parallel axis theorem to determine moments of inertia about the axis of rotation. The skaters are moving as one body with one angular velocity, but they each have their own moments of inertia given relative to their own CoMs. For the man, that’s fine…the axis they’re rotating about passes through his CoM,…In which of the following cases is the magnitude of the total torque about the center of mass largest?
- Consider the following mass distribution where the x- and y-coordinates are given in meters: 5.0 kg at (0.0, 0.0) m, 3.4 kg at (0.0, 3.7) m, and 4.0 kg at (2.9, 0.0) m. Where should a fourth object of 8.6 kg be placed so that the center of gravity of the four-object arrangement will be at (0.0, 0.0) m? X = y = m Need Help? Read It Watch It) The distance between the centers of the wheels of a motorcycle is 155 cm. The center of mass of the motorcycle, including the rider, is 88.0 cm above the ground and halfway between the wheels. Assume the mass of each wheel is small compared with the body of the motorcycle. The engine drives the rear wheel only. What horizontal acceleration of the motorcycle will make the front wheel rise off the ground? (There are a number of views on how to do this online, if you have difficulty with this problem look them up. One view is to calculate the torque about the point of contact on the ground and also the around the center of mass and set them equal to each other.) (a = 8.631 m/s)(a) Calculate the angular momentum (in kg-m2/s) of an ice skater spinning at 6.00 rev/s given his moment of inertia is 0.370 kg-m². ✓kg-m²/s 14 FOR YOUR TEACHER PRACTICE ANOTHER (b) He reduces his rate of spin (his angular velocity) by extending his arms and increasing his moment of inertia. Find the value of his moment of inertia (in kg-my if his angular velocity drops to 1.70 rev/s. x k-m² (c) Suppose instead he keeps his arms in and allows friction with the ice to slow him to 3.00 rev/s. What average torque (in N-m) was exerted if this takes 18.0 seconds? XN-m
- What is the angular momentum of a 3.4-kg uniform cylindrical grinding wheel of radius 24 cm when rotating at 1400 rpm ? How much torque(in magnitude) is required to stop it in 6.0 s ? Express your answer using two significant figuresConsider the following mass distribution where the x- and y-coordinates are given in meters: 5.0 kg at (0.0, 0.0) m, 2.9 kg at (0.0, 3.3) m, and 4.0 kg at (3.5, 0.0) m. Where should a fourth object of 9.4 kg be placed so that the center of gravity of the four-object arrangement will be at (0.0, 0.0) m? x = m y = m