Question

A toy train rolls around a horizontal $1.0$-m-diameter track. The coefficient of rolling friction is $0.10$. How long does it take the train to stop if it’s released with an angular speed of $30$ rpm?

Short answer

The train will take $1.61s$to stop if it’s released with an angular speed of $30rpm$.

Step-by-step solution

Given Information

A toy train rolls around a horizontal $1.0$-m-diameter track. The coefficient of rolling friction is $0.10$.

Explanation

According to the information

Initial speed $\mu =30rpm$

Diameter $d=1.0m$

Radius $R=\frac{1}{2}=0.5$

Convert rpm to rad/s as follow:

$(30rpm)=\left[\frac{30\left(2\pi \right)}{60}\right]$

$=3.15rad/s$

The time take is expressed as follow:

$T=\frac{3.15}{1.96rad/s^2}$

$T=1.61s$

Final Answer

The train will take $1.61s$to stop if it’s released with an angular speed of$30rpm$.