## Statement

difficulty A toy train nicknamed "torpedo" moves in a circular trajectory of 2 m radius without possibility of changing its linear velocity. Knowing it takes 10 seconds for a full rotation, calculate:

a) Its angular and linear velocities.
b) The angle and the distance traveled in 2 minutes.
c) Its acceleration.

## Solution

We have a uniform circular motion because the trajectory is a circumference and the speed does not change throughout the motion.

Question a)

Data

R = 4 m
T = 10 s

Resolution

To calculate the angular velocity, we will use the following expression:

And the linear velocity is:

Question b)

Data

ω = 0.628 m
t = 2 min = 120 s
R = 2 m
φ0 = 0 rad (assume that the initial angle is 0 rad).
s0 = 0 m (assume that the initial distance traveled is 0 m).

Resolution

To calculate the angle covered:

and the distance traveled:

Question c)

Since we are dealing with a u.c.m. the values of the accelerations that we can calculate in this type of motion are:

## Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

Formulas
Related sections
$\phi ={\phi }_{0}+\omega ·t$
$\alpha =0$
$s=\phi ·R$
${a}_{n}=\frac{{v}^{2}}{R}={\omega }^{2}·R$
$v=\omega ·R$
${a}_{t}=0$