Question

A truck with 0.420 m radius tires travels at 32 m/s. What is the angular velocity of the rotating tires in radians per second? What is the angular velocity of the rotating tires in rev/min?

Answer 1

76 rad/sec 730 rev/min First, calculate the circumference of the tires which is 2*pi*r 2*pi*r = 2 * 3.14159 * 0.420 m = 2.6389 m Now divide the velocity by the circumference 32 m/s / 2.6389 m = 12.1261 rev/s Since there are 2*pi radians for the circumference, multiply by 2*pi to get the number of radians per second. 12.1261 rev/s * 2 pi rad/rev = 76.19 radians/sec Since you only have 2 significant figures, round to 76 rad/sec Now to get rev/min, take the earlier computed value of 12.1261 rev/s and multiply by 60 12.1261 rev/sec * 60 sec/min = 727.5661 rev/min Once again, round to 2 significant figures, so 730 rev/min

Answer 2

Answer :
`\omega=76.19\ radians/second` and
`\omega=727.55\ rev/min`

Explanation :

It is given that,

The radius of the truck, r = 0.420 m

Velocity of the truck, v = 32 m/s

We have to find the angular velocity of the rotating tires.

The relation between the angular velocity and the linear velocity is :

`v=r\omega`

`\omega` is the angular velocity

`\omega=(v)/(r)`

`\omega=(32\ m/s)/(0.420\ m)`

`\omega=76.19\ radians/second`

We know that, 1 revolution = 2π radian

So,
`\omega=727.55\ rev/min`

Hence, this is the required solution.