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- 18) Consider an adult and a child riding their bikes. The adult's bicycle has tires with an outer diameter of 700 centimeters. The child's bicycle has tires with an outer diameter of 350 centimeters. The adult bicycle's tires are rotating with an angular velocity of 4.0 radians per second. If the child cyclist is traveling along the road at the same speed as the adult, then what angular velocity must the child's bicycle's tires be rotating at? [Assume the tires are rotating without slipping as the cyclists ride]. A) 1.0 radians second per B) 2.0 radians per second C) 4.0 radians per second D) 8.0 radians per second E) 16.0 radians per second abnoose e GA solid sphere, made of acrylic plastic with a density of 1.1 g/cm3,1.1 g/cm3, has a radius of 5.0 cm.5.0 cm. A very small "eyelet" is screwed into the surface of the sphere and a horizontal support rod is passed through the eyelet, allowing the sphere to pivot around this fixed axis, as shown in the figure. If the sphere is displaced slightly from equilibrium on the surface of Earth, determine the period ?T of its harmonic motion when it is released.let's consider the three atoms composing the molecule have different masses and coordinate, while the axis of rotation is still y-axis. The first atom has a mass of 8.61 kg, with x coordinate at 3.063 m and y coordinate at 3.826 m. The second atom has a mass of 63.048 kg, with x coordinate at 87.738 m and y coordinate at 51.326 m. The third atom has a mass of 26.317 kg, with x coordinate at 42.334 m and y coordinate at 23.115 m. What is the moment of inertia in the unit of kg m2 with respect to the y axis?
- A ceiling fan consists of a small cylindrical disk with 5 thin rods coming from the center. The disk has mass md = 2.7 kg and radius R = 0.25 m. The rods each have mass m, = 1.2 kg and length L = 0.86 m.Our Sun has a radius of about 695,800 km and a mass of about 2.0 × 1030 kg, and rotates around its axis about once every 29 days.Calculate the rotational velocity of the Sun.Calculate the linear speed of particles on the outermost portion of the Sun.Calculate the angular acceleration, tangential acceleration, and radial acceleration of the Sun.Calculate the rotational (angular) momentum of the Sun, modeled as a uniform solid sphere. The rotational inertia of a solid sphere is (2/5)MR2.Imagine that without any external objects interacting with it, the Sun were to collapse to the size of a neutron star, with a radius of about 15 km–about the size of Manhattan Island.What would be its rotational inertia when it was finished collapsing?What would be its rotational momentum when it was finished collapsing?In what time interval would the Sun complete one rotation around its axis after it was finished collapsing1. The horizontal circular platform weighs 500 lb and has a radius of gyration of kz = 8 ft from the z-axis passing through O. The platform is free to rotate about the z-axis and is initially at rest. A person having a weight of 150 lb begins to run along the edge in a circular path of radius 10 ft. If they maintain a speed of 4 ft/s relative to the platform, determine the angular velocity of the 10 ft platform. Neglect friction. I don't think we have dealt with relative velocity in this context, but it follows our earlier relative velocity treatment. Here all speeds are in the t-direction. vp is the speed of the person, and vp is the speed of the disk at the location of the person. Then vp = vp + Vp/D, same as before. You are given vpp = 4 ft/s.
- A uniform solid sphere of mass 6.0 kg and radius 10 cm is rolling without slipping along a horizontal surface with a speed of 4.9 m/s (this is the speed of the center of mass) when it starts up a ramp that makes an angle of 30° with the horizontal. 1st а) b) While the ball is moving up the ramp, find What is the maximum distance it can go up the ramp, measured along the surface of the ramp? 2nd? the acceleration (magnitude and direction) of its center of mass and i) ii) | 3rd 3] the friction force (magnitude and direction) acting on it due to the surface of the ramp. Moment of inertia of a solid sphere is I em =MR². стWhat is the solution of this problem?