During 0.21 s, a wheel rotates through an angle of 2.10 rad as a point on the periphery of the wheel moves with a constant speed of 2.12 m/s. What is the radius of the wheel?

d = 2.12m/s * 0.21s = 0.4452 m.

C=(6.28rad/2.10rad) * 0.4452 m=1.33 m. =
Circumference.

C =3.14 * 2r = 1.33 m.
6.28r = 1.33
r = 0.212 m. = Radius of the wheel.

Well, if you want me to be relevant, I suppose I could tell you that the formula to calculate the radius of a wheel is to divide the angular displacement by the time taken. In this case, the angular displacement is 2.10 rad and the time taken is 0.21 seconds. So, dividing 2.10 by 0.21 would give you the value of the radius. But hey, why calculate when you can just spin your way to the answer? Wheeee!

To find the radius of the wheel, we can use the formula for linear speed:

v = r * ω

where v is the linear speed, r is the radius of the wheel, and ω is the angular velocity.

We are given:
- ω = Δθ / Δt = 2.10 rad / 0.21 s = 10 rad/s
- v = 2.12 m/s

Substituting these values into the formula, we can solve for the radius:

2.12 m/s = r * 10 rad/s

Divide both sides of the equation by 10 rad/s:

r = 2.12 m/s / 10 rad/s

r ≈ 0.212 m

So, the radius of the wheel is approximately 0.212 meters.

To find the radius of the wheel, we can use the formula:

Arc Length = Radius × Central Angle

In this case, the arc length is the distance traveled by the point on the periphery of the wheel, which is given as 2.12 m/s for 0.21 s. Thus, the arc length is:

Arc Length = ( 2.12 m/s ) × ( 0.21 s ) = 0.4452 meters

The central angle is the angle that the wheel rotates through, which is given as 2.10 rad.

Now, we can rearrange the formula to solve for the radius:

Radius = Arc Length / Central Angle

Substituting the values we have:

Radius = 0.4452 meters / 2.10 rad ≈ 0.212 meters

Therefore, the radius of the wheel is approximately 0.212 meters.