A solid sphere of mass My radius R is released from a ramp that has a height "h" If the sphere rolls without sliding, in terms of g and h determine the velocity of the center of mass of the sphere at the base of the ramp. Justify your process

A disk of mass M, radius R, is rolling down an incline dragging a box mass M attached with alight rod to attached at the center of the disk. The friction coefficients are the same for both masses: . Draw free body diagrams for each object. Determine the liner acceleration of the box. Determine the friction force acting on the disc. Determine the tension in the rod.

You have a summer internship at NASA and are working on plans for a new space station to be launched into orbit around the Earth. The design of the space station is shown. i It is to be constructed in the shape of a hollow ring of mass 52,000 kg. The structures other than the ring shown in the figure have negligible mass compared to the ring. Members of the crew will walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius r = 140 m. The thickness of the ring is very small compared to the radius, so we can model the ring as a hoop. At rest when constructed, the ring is to be set rotating about its axis so that the people standing inside on this deck experience an effective free-fall acceleration equal to g. The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring. Your supervisor asks you to determine the following: (a) the time interval during which the rockets must be fired if each…

A yoyo of radius R and mass M is released from rest with the string vertical and its top end fixed up a support as shown below. How fast is the center of mass of the yoyo moving when it has fallen a distance of 47 cm. Ignore the mass of the string and express your answer if m/s

Conservation of Angular Momentum Given data on two disks, such as masses and inner/outer diameters/radii, and the initial angular velocities of the 2 disks, use the conservation of angular momentum principle to calculate the common angular velocity after the two disks are allowed to contact each other and spin together. Or, given the common final angular velocity, solve for unknowns such as the initial angular velocity of one of the disks. Or, given data on the starting and final angular velocities and some data on the disks, solve for unknowns such as moments of inertia, masses or diameters/radii. EXAMPLE Two metal disks have masses m1=3.45 kg and m2=UNKNOWN kg, and each has a radius of 8.31 cm. (You may ignore the inner hole for both disks assume that it is very small.) They spin on cushions of air in a standard rotational dynamics apparatus. Initially, disk #1 is spinning counterclockwise at 6.02 rad/s and disk #2 is spinning clockwise at 2.50 rad/s. A pin is removed that drops disk…

72. A body of mass m and negligible size starts from rest and slides down the surface of a frictionless solid sphere of radius R. (See below.) Prove that the body leaves the sphere when 0 = cos¹ (2/3). R

With a speed of v(initial), a perfectly rounded mass ball as known as “m” is moving towards the left and touches a uniform disc of mass as known as M and radius as known as R which is covered in super glue that instantly sticks whatever it touches and is pivoted about its center. Find the answers to the following questions How fast is the whole system rotating after the collision? Before coming to rest, to what angle will the system rotate?

A ball with an initial velocity of 8.61 m/s rolls up a hill without slipping. (a) Treating the ball as a spherical shell, calculate the vertical height (in m) it reaches. (b) Repeat the calculation (in m) for the same ball if it slides up the hill without rolling. m Additional Materials O Reading