How Does Rolling Friction Affect a Toy Train's Motion on a Circular Track?

[popo]

Hi, thanks for taking a look!

A toy train rolls around a horizontal 1.4-m-diameter track. The coefficient of rolling friction is 0.12.
(a) What is the magnitude of the train's angular acceleration after it is released?
(b) How long does it take the train to stop if it's released with an angular speed of 16 rpm?

I think I know which equations to use: α = ω^2*r and a = rα, but there is no mention of velocity in the problem so I am stuck.

 

[tony873004]

Use Newton's 2nd law to get tangential acceleration. Then your 2nd formula translates it into angular acceleration.
There's a homework help forum a few links up from this one for questions like this.

 

[popo]

then my question would go to why we use tangential acc instead of centripetal acc?

 

[popo]

I know we want to find angular acc so we need to use a = rα, which that is tangential acc, but the thing is the train is moving in ciruclar motion so there should only be centripetal forces acting on it which would be the friction.

 

[tony873004]

The rolling resistance is not acting as a centripetal force. It is tangential.

 

[popo]

is that a special case? because from what i learn for circular motion there would be friction force acting centripetally or centrifugally.

 

[tony873004]

Yes, but that's not the rolling resistance. The tracks are providing a centripetal force. In the case of a car, it is static friction causing the centripetal acceleration, and rolling resistance causing the car to lose speed. In the case of a train, it is a normal force acting towards the center of the curve that acts as the centripetal force. Rolling resistance just slows it down.

 

[popo]

Okay now i get you, but just want to be clear that i have the same picture about the train. How does the track looks like? It said horizontally so is that like a circular train on a horizontal flat surface?

 

[popo]

I appreciate you help by the way

 

[tony873004]

Yes, horizontal just means flat ground here.
Your welcome!

 

[sophiecentaur]

but there is no mention of velocity

it's released with an angular speed of 16 rpm

Angular speed will tell you the tangential velocity if you know the radius of the track.