Question

1) A wheel with a weight of 396 N comes off a moving truck and rolls without slipping along a highway. At the bottom of a hill it is rotating at an angular velocity of 27.5 rad/s . The radius of the wheel is 0.584 m and its moment of inertia about its rotation axis is 0.800 MR2. Friction does work on the wheel as it rolls up the hill to a stop, at a height of h above the bottom of the hill; this work has a magnitude of 3550 J .

Calculate h.

Use 9.81 m/s2 for the acceleration due to gravity.

2) A hollow spherical shell with mass 2.45 kg rolls without slipping down a slope that makes an angle of 38.0 ∘ with the horizontal.

Part A

Find the magnitude of the acceleration acm of the center of mass of the spherical shell.

Take the free-fall acceleration to be g = 9.80 m/s2 .

Part B

Find the magnitude of the frictional force acting on the spherical shell.

Take the free-fall acceleration to be g = 9.80 m/s2 .

Answer 1

now solution for the second part i.e. spherical shell::

above is the proof required and below is the solution for 2::::