2- An object of mass M and moment of inertia / is rolling without slipping from inclined plane, find the following (a) Number of degrees of freedom (DoF) (b) The kinetic energy T and the potential V energy. (c) The Lagrangian L of the system. (d) The equation of motion
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- A car initially traveling at 24.2 m/s undergoes a constant negative acceleration of magnitude 1.80 m/s2 after its brakes are applied (a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tire have radii of 0.305 m? rev (b) What is the angular speed of the wheels when the car has traveled half the total distance? rad/s Need Help? Read It1) A solid sphere and a hollow cylinder are both rolling without slipping along a smooth horizontal surface at a translational speed of v = 6.35 m/s. They then encounter a hill. hmax a) Which object reaches a larger maximum height above the level ground? b) What is the maximum height the object from Part A reaches?A person of mass 78 kg stands at the center of a rotating merry-go-round platform of radius 2.9 m and moment of inertia 840 kg⋅m2 . The platform rotates without friction with angular velocity 0.95 rad/s . The person walks radially to the edge of the platform.a) Calculate the angular velocity when the person reaches the edge. b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person's walk.
- A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 12.0 rev/s; 45.0 revolutions later, its angular speed is 18.0 rev/s. Calculate (a) the angular acceleration (rev/s²), (b) the time required to complete the 45.0 revolutions, (c) the time required to reach the 12.0 rev/s angular speed, and (d) the number of revolutions from rest until the time the disk reaches the 12.0 rev/s angular speed. (a) Number i Unit (b) Number i Unit (c) Number i Unit (d) Number i Unit211.) A disk, a solid sphere, and a ring, all with radius 0.4 m and with masses of 2 kg, roll along the path shown in the figure below. They all are initially rolling such that their center of mass velocities are all equal to 3 m/s. Rank in order, from smallest to greatest, the heights that these shapes achieve on the incline. (Assume friction is present to roll appropriately, but negligible enough to exclude otherwise. They all start at the same position but are separated in the picture to demonstrate the differences in shape.) h A) hdiskProblem A) At a circus you see a man spinning plates with radii of 75 cm on top of long poles. The plates have a constant angular acceleration of 0.6 rad/s?. Assuming the plates start from rest, after a time of 8 seconds calculate a) how many revolutions they have made, b) their angular velocity, c) their tangential acceleration, d) their radial acceleration, and e) their overall acceleration, magnitude and direction with respect to the edge of the disk.A uniform solid sphere of mass 12.0 kg and radius 7.0 cm rotates at 300 revolutions per minute (rpm) on an axis passing through its center. Calculate: a) Its moment of inertia b) Its rotational kinetic energy c) The angular momentum (L), that is, the magnitude of the product Iw, in the appropriate IS units d) Based on the general definition of the moment of inertia (I = Mr²), determine the radius of gyration of the sphere around the axis that passes through its center.4. A homogeneous, rigid cylinder of mass M and radius R is placed on a М,R small rectangular plate of mass m. There is sufficient static friction between the cylinder and the plate. The plate itself is placed on a flat, frictionless table. A constant force of magnitude F is applied to the plate in direction parallel to the table as shown on the diagram. Once the force F is applied, the cylinder goes immediately into pure rolling F т (no slipping or skidding). Find: a. The translational (linear) acceleration of the block, ap. b. The angular acceleration of the cylinder, a. c. The translational (linear) acceleration of the cylinder ac. Given variables: M, R, m, F