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A sphere of mass ma and radius r rolls without slipping inside a curved surface of radius R. Knowing that the sphere is released from rest in the position shown, derive an expression for (a ) the linear velocity of the sphere as it passes through B (b) the magnitude of the vertical reaction at that instant.
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- A 2.60-kg hoop 1.80 m in diameter is rolling to the right without slipping on a horizontal floor at a steady 2.70 rad/s . Find the magnitude of the velocity vector of each of the following points, as viewed by a person at rest on the ground: (i) the highest point on the hoop; (ii) the lowest point on the hoop, (iii) a point on the right side of the hoop, midway between the top and the bottom. Find the magnitude of the velocity vector for each of the points in part C, except as viewed by someone moving along with same velocity as the hoop.A small sphere of radius ro = 1.5 cm rolls without slipping on Γο the inside of a track of radius R₁ = 26 cm. If the small sphere starts from rest at the vertical edge of the track, (a) what will be its speed when it reaches the lowest point of the track? When it leaves the track after passing through an angle of 135°, (b) what will be its speed, and c) at what distance D from the base of the track will the sphere hit the ground? (The rotational inertia of a small sphere about its center of mass is I=2mr2/5. Ro 135° Ro. D Hint: Don't forget the radius of the sphere when looking at gravitational potential energy! (a) v1.85 m/s, (b) v' = 1.56 m/s, c) D= 0.478 m.A bicycle tire is 66 cm in diameter. (a) At what frequency f does the tire rotate when the bicycle is traveling at a speed of 35 km/h? (b) What is the angular frequency ω?
- In a conical pendulum, mass of the bob 19 0.5gm and length of the string is 20 cm. The bob describes a horizontal circle of radius 10 cm. Calculate its angular speed.Please solve (d) and (e)Question 6: The particle has a mass of 0.5 kg and is confined to move along the smooth horizontal slot due to the rotation of the arm OA. Determine the force of the rod on the particle and the normal force of the slot on the particle when 0 = 30°. The rod is rotating with an angular acceleration of Ö= 3 rad/s2 when e= 2 rad/s at 0 = 30°. Assume the particle contacts only one side of the slot at any instant. A ở = 2 rad/s 0.5 m