a 7kg solid sphere rolls without slipping on a horizontal surface with its center of mass moving at 5m/s. what is the ratio between the translational and the rotational kinetic energies?
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a 7kg solid sphere rolls without slipping on a horizontal surface with its center of mass moving at 5m/s. what is the ratio between the translational and the rotational kinetic energies?
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- You are riding your bicycle down the street at a speed of 16 m/s. Your bicycle's frame has a mass of 6.0 kg, and each of its two wheels has mass 2.2 kg and radius 0.34 m. Each wheel can be thought of as a hollow hoop (assuming that the rim has much larger mass than the spokes). What is the total kinetic energy of the bicycle (in Joules)?(take into account both the translational and rotational motion.)A 70 kg disk is spinning about a vertical axis of rotation with a radius of 1.2 m and a rotational inertia of 0.45 mr2 and it has an initial angular velocity of 10 rad/s. An unknown mass falls onto the disk 0.8 m away from the axis of rotation. After the collision, the disk is now spinning at 6 rad/s. The rotational inertia of the mass is mr2. Calculate the unknown mass that falls on the disk.A uniform solid ball rolls without slipping down a plane which is inclined at 31° to the horizontal. If the ball has a radius r=0.4m, a mass m=0.1 kg and starts from rest, find: a) the speed of the ball after it travels 2m down the incline. b) at this point, what is the angular momentum of the ball? c) If the coefficient of friction between the ball and the plane is 0.25, what is the maximum angle of inclination that allows the ball to roll without slipping?
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- A solid cylinder (disk) and a hollow cylinder are rolling with the same center- of-mass velocity v = 2 m/s on a level surface towards an incline. Both R cylinders have the same radius R and mass M. The moments of inertia are: 1 Solid cylinder 1, MR² Hollow cylinder I, = MR² (a) What is true about the kinetic energy when the cylinders are rolling on level ground? (i) they have the same translational kinetic energy (ii) they have the same rotational kinetic energy (iii) they have the same total kinetic energy [1] only (i) [2] only (ii) [3] (i) and (ii) [4] (i) and (iii) [5] (i), (ii), and (iii) (b) Which conservation law will allow you to calculate the final height? Conservation of: [1] momentum [5] moment of inertia [2] mechanical energy [3] kinetic energy [4] angular momentum (c) Calculate the maximum height the solid cylinder will reach before it rolls down again; please use g = 10 m/s². (d) Calculate the maximum height the hollow cylinder will reach before it rolls down again.A solid sphere rolls down an incline without slipping. At any instant while in motion, what is the ratio of its rotational kinetic energy about its center of mass to its total kinetic energy?A 2.25 kg solid, uniform disk rolls without slipping across a level surface, translating at 4.00 m/s. If the disk's radius is 0.500 m, find the following. HINT (a) the disk's translational kinetic energy (in J) (b) the disk's rotational kinetic energy (in J)