A uniform solid sphere rolls along a horizontal frictionless surface at 25 m/s and makes a smooth transition onto a frictionless incline having an angle of 300. How far up the incline does the sphere roll when it comes to a momentary stop? Note for a sphere I= 2/5Mr2, where M is the mass of the sphere and r is the radius of the sphere
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A uniform solid sphere rolls along a horizontal frictionless surface at 25 m/s and makes a smooth transition onto a frictionless incline having an angle of 300. How far up the incline does the sphere roll when it comes to a momentary stop? Note for a sphere I= 2/5Mr2, where M is the mass of the sphere and r is the radius of the sphere.
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- A bottle is initially spinning with an angular velocity of ω = 1.5 rad/s. Over the span of t = 3.9 seconds the bottle angularly accelerates with α = 1.5 rad/s2. What is the angular velocity of the bottle after the 3.9 s?A uniform disk of mass 7 kg and radius 0.2 m is free to rotated about an axis perpendicular to its center. A constant force of size 146 N acts at the edge of the disk, in a direction tangent to that edge. The force acts until the disk has completed 169 full rotations. What is the angular momentum of the disk after those rotations are complete, in kg m2/s? It could be useful to you to know that the rotational inertia of a uniform disk is 1/2 M R2. (Please answer to the fourth decimal place - i.e 14.3225)A 24 g block sits at the center of a turntable that rotates at 80 rpm. A compressed spring shoots the block radially outward from the center along a frictionless groove in the surface of the turntable. Calculate the turntable's angular speed when the block reaches the outer edge. Treat the turntable as a solid disk with mass with mass 200 g and diameter 54.0 cm. Express your answer in revolutions per minute.
- John wanted to measure the objects angular speed at the bottom of the hill. He built the inclined frictionless ramp of height d, release the object from the top, and measure the angular speed at the Bottom. First, John released a hollow sphere [Ip(2/3) mr^2] from the rest. The diameter and the mass of the sphere were 317 cm and 45.2 kg, respectively. How much was the angular speed John measures at the bottom of the incline he built. Tip: the object rotates down the incline without slipping. Use following values: d=3.57 m and g=9.80 m/s^2Find the percentages of the total kinetic energy associated with rotation and translation for the following objects that are rolling without slipping. (a) a uniform sphere Krot = % x Ktot Ktrans = % x Ktot (b) a uniform cylinder Krot % x Ktot Ktrans = % x Ktot (c) a hoop Krot = % x Ktot Ktrans = % x Ktot eBookA typical helicopter with four blades rotates at 300 rpm and has a kinetic energy of 2.45 105 J. What is the total moment of inertia, in kg · m2 of the blades?
- A solid disk of uniform density and mass M = 0.950 kg with radius R = 0.250 m is suspended vertically and is free to rotate about its center without friction. A point object that has the same mass as the disk is placed at an angle 0 = 25.0° clockwise from the top along the rim, causing the disk to rotate. The acceleration due to gravity is g=9.81m/s². What is the angular speed wf of the disk when the point object is directly below the center of the disk? R 0.A turntable with a mass of 12 kg and a radius of 2 meters spins at a constant angular velocity of 140 rpm. A 500-gram scoop of uniformly-dense ice cream falls onto the turntable, so the scoop's center of mass is one meter away from the turntable's center. The scoop forms a hemisphere and has a radius of 4 cm. If there's no friction between the brick and ice cream scoop and they spin at the same angular speed, what is their final angular speed, in rev/min or in rad/s? Justify your answer with your rationale and equations used. Moments of Inertia: Idisk =MR for rotation about its center of mass parallel to the z-axis. %3D Ihemisphere = MR for rotation about its center of mass parallel to the z-axis. Edit View Ansert Format Tools Table COREIProblem 1: Consider a small block weighing 200 grams that is placed 10 cm from the center of turntable. The turntable slowly begins to spin. If the static friction coefficient is g = 0.4, at what angular velocity will the block begin sliding off the turntable?
- A solid sphere starts from rest and rolls down a slope that is 6.4 m long. If its speed at the bottom of the slope is 5.3 m/s, what is the angle of the slope? O 21° O 18° 31° O cannot be calculated without knowing the mass and radius of the sphere O 12°A small 0.360-kg object moves on a frictionless horizontal table in a circular path of radius 3.00 m. The angular speed is 4.97 rad/s. The object is attached to a string of negligible mass that passes through a small hole in the table at the center of the circle. Someone under the table begins to pull the string downward to make the circle smaller. If the string will tolerate a tension of no more than 160 N, what is the radius of the smallest possible circle on which the object can move?A uniform solid sphere rolls along a horizontal frictionless surface at 15 m/s and makes a smooth transition onto a frictionless incline having an angle of 300. How far up the incline does the sphere roll when it comes to a momentary stop? Note for a sphere I= 2/5Mr2, where M is the mass of the sphere and r is the radius of the sphere.