Rolling

Front 1

Why is the v(COM) constant?

Back 1

The object has constant speed

Front 2

What distance does the COM travel in a certain time interval dt?

Back 2

s = Rθ

Front 3

How do you calculate v(COM) and v at the top of the body?

Back 3

Front 4

What are the types of kinetic energy?

Back 4

• rotationalfrom rotation about COM
  
• translational from translation of COM

Front 5

How do you derive the kinetic energy from the parallel-axis theorem?

Back 5

Front 6

What is the acceleration of the COM of a body rolling down a ramp?

Back 6

Front 7

Translational acceleration and force of a body rolling down a ramp

Back 7

Front 8

Deriving the acceleration of the COM from the angular acceleration

Back 8

only force causingrotational motion = friction @ P

Front 9

How to derive the velocity of the COM

Back 9

Front 10

What energy changes take place for a yo-yo?

Back 10

• as the yo-yo rolls down, it loses gravitational potential energy
• this energy is transferred into both translational + rotational energy
• as the yo-yo climbs back up → it loses kinetic energy + transfers back to potential
  

Front 11

What assumptions must be made to calculate the acceleration of the COM?

Back 11

• the yo-yo rolls directly down the string so the angular displacement = 0
• it rolls around the axle with radius R0, not the outer radius R
• it is slowed down by tension rather than friction

Front 12

Why does rolling friction occur with surface deformation and a deforming body?

Back 12

• due to the deformations, contact forces no longer act along a single point but over an area
• this means the normal force exerts torque opposing rotation
• there is some sliding over the surface
• because of the deformation, mechanical E is lost