Aim: How do we explain the rolling motion of rigid bodies?

Kinetic Energy of Rolling Body Kinetic Energy of Rolling Body K = ½ mvcm2 +1/2Iω2

Diagram of Rolling body

Freebody Diagram of Rolling Body

Thought Question Which arrives at the bottom first: A ball rolling without sliding down incline A or a box of the same mass as the ball sliding down a frictionless incline B having the same dimensions as incline A? The box sliding down incline B because it converts all of its gravitational potential energy into translational kinetic energy

Thought Question 2 A cylinder (I=1/2MR2), a sphere (I=2/5 MR2), and a hoop (I=MR2) roll without slipping down the same incline, beginning from rest at the same height. All three objects share the same radius and total mass. Which object has the greatest kinetic energy at the bottom of the incline? They all have the same kinetic energy at the bottom Which object has the greatest translational kinetic energy…? The sphere has the greatest translational kinetic energy because it has the smallest moment of inertia Which object has the greatest rotational kinetic energy? The hoop has the greatest rotational kinetic energy because it has the greatest moment of inertia

Thought Question 2

Problem 1 A metal can containing condensed mushroom soup has a mass of 215 g, a height of 10.8cm, and a diameter of 6.38 cm. It is placed at rest on its side at the top of a 3 m long incline that is 25 degrees to the horizontal and then released to roll straight down. Assuming energy conservation, calculate the moment of inertia of the can if it takes 1.50 s to reach the bottom of the incline. Which pieces of data are unncessary for calculating the solution? 1.21 x 10^-4

h=sinθ=3sin25

Problem 2 If the object shown below is a solid sphere, Calculate the speed of mass at the bottom. Determine the magnitude of the translational acceleration of the center of mass.

Problem 3 A cylinder of mass 10 kg rolls without slipping on a horizontal surface. At the instant its center of mass has a speed of 10 m/s, determine The translational kinetic energy of its center of mass The rotational energy about its center of mass Its total energy 500 J b)250 J c) 750 J

Problem 4 Which object requires the greatest coefficient of friction to keep it from slipping? The hoop requires the greatest coefficient of friction to keep from slipping because it requires the greatest torque to accelerate. Torque= Moment of Inertia*Angular Acceleration=Static Friction*Radius=Coefficient of Friction *Normal Force*Radius Hoop

Problem 5 A disc of mass M, radius R, Icm = 1/2MR2 is rolling down an incline dragging a mass M attached with a light rod to a bearing at the center of the disc. The friction coefficients are the same for both masses, µs and µk. Draw freebody diagrams for each mass. Determine the linear acceleration of the mass M. Determine the friction force acting on the disc. Determine the tension in the rod.

Problem 5