Two disks of equal mass but different diameter are connected with an axle system that allows them to roll down an incline together. Both disks start and finish at the same time.Which of the following statements best describes the disks?
(A) Their tangential velocity is the same.
(B) Their tangential acceleration is the same.
© Their angular velocity is the same.
(D) Their angular displacement is the same.
(E) Their angular acceleration is the same.
According to the book, the answer is (A). But, I don’t see why (B) is incorrect.
I can eliminate C, D, and E due to the fact that angular acceleration = rFsin(theta) / (Mr^2/2)
Since they have equal mass, the friction force causing the torque would be the same due to equal normal force
Hence, tangential acceleration = r * angular acceleration which means that both would have same tangential acceleration
Is there something wrong in my reasoning?
@17zhangw Where is this problem from?
If such a contraption is viewed from a stationary reference point, then the two wheels have the same tangential velocity at any time, which means they have the same tangential acceleration.
If the velocities are taken using the centers of the disks as reference points, then a point on the outside of the larger disk should have the same tangential speed as a point on the outside of the smaller disk, but the velocities are different…
I’m not an expert in physics, so someone who knows physics can feel free to correct me, but something doesn’t seem quite right about this problem to me.
@MITer94 The problem is from SAT II Peterson’s.
Thanks for the response. I think it’s likely to be an error in the question.
Still, if the velocities are taken using the centers of the disks, why is the velocity different? Wouldn’t the velocity of the COM of each disk be the same due to each covering the same distance in the same amount of time?
@17zhangw Yes, I believe so. But since velocity is a vector, the velocities of two points on the outer surfaces of the disks at any point in time will be different. However I doubt that is what the question is asking…