A hoop rolls (without slipping-so you know there is friction)down an incline and

Question

A hoop rolls (without slipping-so you know there is friction)down an incline and you are given the following: M=mass of the hoop R=radius of the hoop d=length of the incline = 30 degrees angle of the incline g=magnitude of acceleration due to gravity Determine the following only in terms of M,R,d,and g. Showyour work with reasoning. 1) rotational moment of inertia of the hoop about an axesthrough its center of mass an perpendicular to the plane of thehoop                   which Iguessed was merely MR^2..I could be wrong though 2)translational speed of the center mass of the hoop at thebottom of the incline 3) angular speed of the hoop about its center mass at thebottom of the incline 4) translational acceleration of the center mass of the hoopas it rolls down the incline 5) angular acceleration of the center mass "   " 6) torque about the center mass of the hoop that's causing itto accelerate down the incline 7) force of friction acting on the hoop as it rolls down theincline 8)total kinetic energy of the hoop at the bottom of theincline 9) total angular momentum of hoop at bottom of incline I'm stuck please help! Thank you A hoop rolls (without slipping-so you know there is friction)down an incline and you are given the following: M=mass of the hoop R=radius of the hoop d=length of the incline = 30 degrees angle of the incline g=magnitude of acceleration due to gravity Determine the following only in terms of M,R,d,and g. Showyour work with reasoning. 1) rotational moment of inertia of the hoop about an axesthrough its center of mass an perpendicular to the plane of thehoop                   which Iguessed was merely MR^2..I could be wrong though 2)translational speed of the center mass of the hoop at thebottom of the incline 3) angular speed of the hoop about its center mass at thebottom of the incline 4) translational acceleration of the center mass of the hoopas it rolls down the incline 5) angular acceleration of the center mass "   " 6) torque about the center mass of the hoop that's causing itto accelerate down the incline 7) force of friction acting on the hoop as it rolls down theincline 8)total kinetic energy of the hoop at the bottom of theincline 9) total angular momentum of hoop at bottom of incline I'm stuck please help! Thank you

Explanation / Answer

I just need someone to somewhat check my work, and possibly goover if I am getting it wrong. for: 1) I= MR^2 2) i used the equation for the total amount of energy in thesystem: PEmax = total Energy= Ktranslational+ Krotational          Mgdsin=(1/2)MV2 +(1/2) I2          Mgdsin=(1/2) MV2 + (1/2)MR2(V2/R2)             gdsin=(1/2)V2+ (1/2)V2             gdsin=V2                V=gdsin 3)you know =V/R so =(sqrt(gdsin))/R 4) using kinematic equations, V=at and d= (1/2)at2          manipulatedit and found t= 2d/a and plug that back into the equation toget a=V2/2d and we know V2=gdsinso             a=gdsin/2d which then becomes a=gsin/2 5) you know a=R so =a/R              = gsin/2R 6)=mgcosdsin90 Now this is where i get stuck, I am not sure how to find theforce of friction in terms of M R d and g. I know friction ismgcos but there is no so I don't know how tocalculate this.Also, I didnt know if this force of frictionaffected the total kinetic energy at the bottom (#8) so I wasntsure how to work that, along with the titak angular momentum.Please help. I would really appreciate it!          manipulatedit and found t= 2d/a and plug that back into the equation toget a=V2/2d and we know V2=gdsinso             a=gdsin/2d which then becomes a=gsin/2 5) you know a=R so =a/R              = gsin/2R 6)=mgcosdsin90 Now this is where i get stuck, I am not sure how to find theforce of friction in terms of M R d and g. I know friction ismgcos but there is no so I don't know how tocalculate this.Also, I didnt know if this force of frictionaffected the total kinetic energy at the bottom (#8) so I wasntsure how to work that, along with the titak angular momentum.Please help. I would really appreciate it!

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