A solid sphere with a mass of 1.0 kg and radius of 10 cm rolls down an inclined plane that is 1.0 m long and at an angle of 26◦ from the horizontal. The sphere is released from rest at the top of the plane, and it rolls down to the bottom where it continues to roll along a horizontal surface. (a) What is the rotational speed of the sphere at the bottom of the plane? (b) What is the angular momentum of the sphere at the bottom of the plane? (c) How many revolutions does the sphere make if it rolls along the horizontal surface for 25 s before coming to a stop? Hint: you can assume the acceleration of the sphere along the horizontal surface is constant.

A solid sphere with a mass of 1.0 kg and radius of 10 cm rolls down an inclined plane that is 1.0 m long and at an angle of 26◦ from the horizontal. The sphere is released from rest at the top of the plane, and it rolls down to the bottom where it continues to roll along a horizontal surface. (a) What is the rotational speed of the sphere at the bottom of the plane? (b) What is the angular momentum of the sphere at the bottom of the plane? (c) How many revolutions does the sphere make if it rolls along the horizontal surface for 25 s before coming to a stop? Hint: you can assume the acceleration of the sphere along the horizontal surface is constant.

Similar questions

A uniform cylinder of radius 10 cm and mass 20 kg is mounted so as to rotate freely about a horizontal axis that is parallel to and 5.0 cm from the central longitudinal axis of the cylinder. (a) What is the rotational inertia of the cylinder about the axis of rotation? (b) If the cylinder is released from rest with its central longitudinal axis at the same height as the axis about which the cylinder rotates, what is the angular speed of the cylinder as it passes through its lowest position?
A solid ball of mass 0.10 kg and radius 2.8 cm is released from rest on a no-slip surface at a height of 0.75 m above the bottom of the track, as shown. After reaching its lowest point, the ball begins to rise again, this time on a frictionless surface. Find: a) the ball's angular speed when it is on the frictionless side of the track and b) the height ball rises on the w = 120 rad/s; h = 0.54 m frictionless side.
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?
A thin stick of mass 0.2 kg and length L = 0.5 m is attached to the rim of a metal disk of mass M = 2.0 kg and radius R = 0.3 m . The stick is free to rotate around a horizontal axis through its other end (see the following figure). (a) If the combination is released with the stick horizontal, what is the speed of the center of the disk when the stick is vertical? (b) What is the acceleration of the center of the disk at the instant the stick is released? (c) At the instant the stick passes through the vertical?
A disk of mass M is spinning freely at 4.77 rad/s when a second identical disk, initially not spinning, is dropped onto it so that their axes coincide. In a short time the two disks are corotating. (a)What is the angular speed of the new system (in rad/s)? (b) If a third such disk is dropped on the first two, find the final angular speed of the system (in rad/s).
In the figure, a 0.400 kg ball is shot directly upward at initial speed 51.9 m/s. What is the magnitude of its angular momentum about P, 6.03 m horizontally from the launch point, when the ball is (a) at maximum height and (b) halfway back to the ground? What is the magnitude of the torque on the ball about P due to the gravitational force when the ball is (c) at maximum height and (d) halfway back to the ground? Ball (a) Number Units (b) Number Units (c) Number Units (d) Number Units
A 20-kg piece of steel pipe that is 20 cm in diameter, 80 cm long, and 1 cm thick is rolling toward you at a speed of 3.0 m/s. (a)What is the magnitude and direction of the pipe’s angular velocity vector w? (b)What is the pipe’s rotational energy? (c) What is its total energy K + Urot?
A ceiling fan can accelerate from rest to 2pi rad/s in 8 seconds. (A) what is the angular acceleration of the fan? (B) find the angular displacement of the fan during the first 5 seconds. (C) at the full angular speed of 2pi rad/s find the corresponding tangential speed of a point at the rim of the wing if the radius of the wing is r=0.5m. (D) what is the centripetal acceleration of a point at the rim (r=0.5 m) when the fan reaches full speed? can you give detailed steps please?
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.