<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Skip Navigation

Rolling Energy Problems

Explores equations used to describe the energy of rolling or sliding objects.

Atoms Practice
Estimated6 minsto complete
Practice Rolling Energy Problems
This indicates how strong in your memory this concept is
Estimated6 minsto complete
Practice Now
Turn In
Rolling Energy Problems

You can use energy conservation in rotation problems just like you did in the energy conservation lessons for linear motion. Note that rotating objects also have kinetic energy of rotation and this must be included when accounting for energy conservation.

Key Equations

Einitial=EfinalThe total energy does not change in closed systems



A hoop of mass 1 kg and radius .75 m, begins at rest at the top of a ramp, 3m above the ground. What is it's rotational velocity at the bottom of the ramp if the hoop rolls down the ramp without slipping?

To solve this problem, we'll apply energy conservation to the hoop. The hoop only has gravitational potential energy at the top of the ramp, and it has both rotational and linear kinetic energy at the bottom of the ramp.

EiPEmghmghmgh2gh2ghωωω=Ef=KE+KErot=12mv2+12Iω2=12mv2+12mr2ω2=12m(ωr)2+12mr2ω2=(ωr)2+r2ω2=2ω2r2=ghr=9.8m/s23m.75m=7.2rad/sstart with conservation of energysubstitute the proper value for each energy termsubstitute in the moment of inertia of the hoopwe can put v in terms of omega because the hoop is rolling without slidingnow we will multiply by 2 and divide by m to simplify the equationsolving for ωplug in the known values

Interactive Simulation


  1. Your bike brakes went out! You put your feet on the wheel to slow it down. The rotational kinetic energy of the wheel begins to decrease. Where is this energy going?

  1. The upper pulley has mass of 2kg and a radius of 30cm. The lower pulley has mass of 4kg and a radius of 1.0m. The 12 kg mass is 5m off the ground.
    1. With what velocity will the 12kg mass hit the ground if μk=0?
    2. With what velocity will the 12kg mass hit the ground if μk=0.2?

Review (Answers)

1. The energy goes into the heat generated by the friction between your foot and the tire.

2. a. 5.87m/s b. 4.79 m/s

Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Please to create your own Highlights / Notes
Show More

Image Attributions

Explore More

Sign in to explore more, including practice questions and solutions for Rolling Energy Problems.
Please wait...
Please wait...