A circular disk of radius 30 cm is rotating with an angular velocity of 2 radians / s. What is the tangential velocity of a point on the rim of the disk? What is its centripetal acceleration?
The tangential velocity is R*w = 60 cm/s.
The centripetal acceleration is R*w^2
= 120 cm/s^2
They may want you to convert the answers to m/s and m/s^2
To find the tangential velocity of a point on the rim of the disk, we can use the formula:
Tangential velocity (V) = Angular velocity (ω) * Radius (r)
Given that the angular velocity (ω) is 2 radians/s and the radius (r) is 30 cm, we can substitute these values into the formula:
V = 2 radians/s * 30 cm
Before we calculate the answer, we need to make sure that the units are consistent. The radius is given in centimeters, but radians/s does not have any specific unit of length. However, since radians are a unit-less measure of angle, we can simply multiply the angular velocity by the radius to get the answer in the same units as the radius. Therefore, we do not need to convert the angular velocity from radians/s to any other unit.
Now we can calculate the tangential velocity (V):
V = 2 * 30 cm
V = 60 cm/s
So, the tangential velocity of a point on the rim of the disk is 60 cm/s.
To find the centripetal acceleration of a point on the rim of the disk, we can use the formula:
Centripetal acceleration (a) = (angular velocity (ω))^2 * Radius (r)
Again, substituting the given values into the formula:
a = (2 radians/s)^2 * 30 cm
Similarly to the previous calculation, we don't need to convert the angular velocity since it is already in radians/s.
Now we can calculate the centripetal acceleration (a):
a = 4 radians^2/s^2 * 30 cm
a = 120 cm^2/s^2
So, the centripetal acceleration of a point on the rim of the disk is 120 cm^2/s^2.