A ring with radius r and mass m roll downhill without slipping as shown in the...
A thin ring of radius R and mass M rolls without slipping along a level track. It has an initial linear, or translational velocity (of the center of gravity) of 3.50 m/s. The ring rolls to the end of the track, where the track curves upward. The center of gravity of the ring rises to a maximum height h above its initial level. Note that V is the symbol for the linear, or translational velocity (of the center of gravity)...
Problem 4. A solid sphere of mass m and radius r rolls without slipping along the track shown below. It starts from rest with the lowest point of the sphere at height h 3R above the bottom of the loop of radius R, much larger than r. Point P is on the track and it is R above the bottom of the loop. The moment of inertia of the ball about an axis through its center is I-2/S mr. The...
A homogeneous ring of radius R and mass m can roll on a horizontal surface without slipping. It is attached at the center to a spring of elastic constant k and rest length 1, and can oscillate on the horizontal plane. See the figure below for a schematic presentation. k (i) What is the number of degrees of freedom of the system? [2] (ii) Compute the moment of inertia of the ring about an axis perpendicular to it and going...
a hoop of mass m and radius r is allowed to roll YANG, YUXI Exam Code 2=MR Line 9. A uniform solid cylinder of radius Rand a thin uniform spherical shell of radius R without slipping. If both objects have the same mass and the same kinetic energy, what the ratio of the linear speed of the cylinder to the linear speed of the spherical A. 4/ K A 22w tingh + RU SMR RMHEA) C. 2/3 D. V10/3 =...
1) A solid ball of mass M and radius R rolls without slipping down a hill with slope tan θ. (That is θ is the angle of the hill relative to the horizontal direction.) What is the static frictional force acting on it? It is possible to solve this question in a fairly simple way using two ingredients: a) As derived in the worksheet when an object of moment of inertia I, mass M and radius R starts at rest...
Problem 4. A solid sphere of mass m and radius rrolls without slipping along the track shown below. It starts from rest with the lowest point of the sphere at height 3R above the bottom of the loop of radius R, much larger than r. Point P is on the track and it is R above the bottom of the loop. The moment of inertia of the ball about an axis through its center is I-2/5 mr. The ball should...
20. A disc of mass m and radius r rolls down an inclined plane without slipping from rest at a height h. The speed of its centre of mass, when it reaches the bottom, is : 21. A particle is located on the x axis at x = 2.0 m from the origin. A force of 25 N, directed 30° above the x axis in the x-y plane, acts on the particle. What is the torque about the origin on...
A small solid porcelain sphere, with a mass m and radius r, is placed on the inclined section of the metal track shown below, such that its lowest point is at a height h above the bottom of the loop. The sphere is then released from rest, and it rolls on the track without slipping. In your analysis, use the approximation that the radius r of the sphere is much smaller than both the radius R of the loop and...
Problem 9 m,r A solid ball of mass m and radius r sits at rest at the top of a hill of height H leading to a circular loop-the loop. The center of mass of the ball will move in a circle of radius R if it goes around the loop. The moment of inertia of a solid ball is Ibull--mr. (a) Find an expression for the minimum height H for which the ball barely goes around the loop, staying...
A solid sphere of mass m and radius R rolls down a parabolic path PQR from height H without slipping (assume R « H) as shown in the figure below. Path PQ is rough (and so the shell will roll on that path), whereas path QR is smooth, or frictionless (so the shell will only slide, not roll, in this region). Determine the height h above point Q reached by the shell on path QR. (Use the following as necessary:...