If the rotational speed of each wheel is 9 revolution per second, what are the tangential speeds of a point on the rim of each wheel?
Note: Wheels spin independently with equal rotation speeds
-Diameter of Wheel A: 24
-Diameter of Wheel B: 12
To find the tangential speed of a point on the rim of a wheel, you need to know the diameter of the wheel and the rotational speed in revolutions per second.
For wheel A with a diameter of 24, the radius is half of the diameter, which is 12 units. Since the wheel is spinning 9 times per second, the tangential speed can be calculated by multiplying the circumference of the wheel by the number of revolutions per second.
The circumference of a circle is given by the formula C = 2πr, where r is the radius. So, for wheel A, the tangential speed (v) is:
v = C * revolutions per second
v = 2π * 12 * 9
Simplifying further:
v = 216π
Therefore, the tangential speed of a point on the rim of wheel A is 216π units per second.
For wheel B with a diameter of 12, the radius is 6 units. Since the wheel is spinning 9 times per second, the tangential speed can be calculated in the same way as for wheel A:
v = 2π * 6 * 9
v = 108π
Therefore, the tangential speed of a point on the rim of wheel B is 108π units per second.