# Drawing Free Body Diagrams with torque

#### juggalomike

1. Homework Statement
This is a review problem i was given for my final exam tommorow, I am stuck on 1 problem, even with the answer key im not understanding it.(also sorry but the picture wont copy from MSword, but its a cylinder rolling up a hill)

(B) When the lander hits the surface, it eventually stops bouncing and finds itself rolling up the side of a crater wall inclined at an angle of theta, still wrapped in its airbags.

To a good first approximation, the lander is a uniform cylinder of mass M and radius R. The airbags can be thought of as forming a thin shelled sphere of radius r and mass m around the lander. Assume that the lander is rolling up the steepest incline possible without slipping. It terms of the given quantities, show a good step-by-step method to find out what the acceleration of the lander will be. Use g of Mars for the acceleration due to gravity on the surface of Mars.

Draw FBD
∑F ⃗ =ma ⃗

Direction of acceleration is down along the incline (+), direction of alpha=out of page
∑τ ⃗ =Iα ⃗

Forces parallel to the incline: +mg∙sin(theta)−fs=ma
Forces perpendicular to incline: +FN − mg∙cos=0
Torques about center of mass: fs∙r = I*alpha
Moment of Inertia I = ½ MR2 + (2/3)∙mr2
Rolling condition: a = r*alpha

Substitute and solve for a: a=(mg∙sinθ)/((I/r^2 +m))

2. Homework Equations

given above

3. The Attempt at a Solution

The part that i dont understand is how they are going from a = r*alpha to a=(mg∙sinθ)/((I/r^2 +m)), i am not seeing what they could be doing to get that answer. Any help is GREATLY appreciated, thanks.

Related Introductory Physics Homework Help News on Phys.org