calculate the linear velocity of an object rotating at an angular velocity "w" at distance "r" from the center . express the answer in centimeter per second.

Question

1.r=10cm; w=20πrad/second
2.r=5cm; w=20πrad/second
3.r=12cm; w=25πrad/second
4.r=30cm; w=8πrad/second

Answer 1

the distance s is

s = rθ

so, the speeds are

ds/dt = r dθ/dt

Your w is just dθ/dt, so plug in the numbers to get ds/dt

Answer 2

I guess I should not have phrased it in that way.

The distance traveled is rθ, so divide rθ by the time it takes to travel through θ. That is, the linear speed v is

v = rw

Note the units

v (cm/s) = r(cm) * w (1/s)