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.
1.r=10cm; w=20πrad/second
2.r=5cm; w=20πrad/second
3.r=12cm; w=25πrad/second
4.r=30cm; w=8πrad/second
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
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)
To calculate the linear velocity of an object rotating at an angular velocity at a specific distance from the center, we can use the formula:
Linear velocity (v) = Angular velocity (w) * Radius (r)
Given that the angular velocity is in radian per second and the radius is in centimeters, we can plug in the values and calculate the linear velocity in centimeters per second for each case:
1. r = 10 cm, w = 20π rad/second
v = (20π) * 10
v = 200π cm/second
2. r = 5 cm, w = 20π rad/second
v = (20π) * 5
v = 100π cm/second
3. r = 12 cm, w = 25π rad/second
v = (25π) * 12
v = 300π cm/second
4. r = 30 cm, w = 8π rad/second
v = (8π) * 30
v = 240π cm/second
Hence, the linear velocities for the given cases are:
1. 200π cm/second
2. 100π cm/second
3. 300π cm/second
4. 240π cm/second