Dimensional Analysis?

[xocandii]

I'm having a trouble with these 3 problems on dimensional analysis. If anyone can help and show how to solve these, I'd be so grateful. Thanks in advance

1. Radius of 10 cm turns at 6 revolutions per second. What is the linear velocity in meters per second?
2. A gear with a 4.6 cm radius turns 3 revolutions per second. What is the linear velocity in cm per second?
3. A roller has a radius of 12.5 and turns 3 revolutions per second. What is the linear velocity of gear in cm per second?

 

[daon2]

Understand that velocity is distance divided by time (and with it a plus or minus sign to give direction). So meters/seconds, or cms/minutes, miles/hours.

For the first one, you have 6 revolutions/second and want to know how many meters/second this is.

Only one conversion is necessary. If x is the number of meters in one revolution, then we have: x meters/revolution = 1.

So 6 revolutions/second = 6 revolutions/second * x meters/revolution = (6x) meters/second.

So if you find x, there is your answer. So how many meters are there in one revolution? Think about the circumference of that circle.