A flywheel turns at 600 rpm. Compute the angular speed at any point on the wheel and the tangential speed 0.5 m from the centre.
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To compute the angular speed at any point on the wheel, we need to understand that the angular speed of a rotating object is measured in radians per second (rad/s).
1. Convert the revolutions per minute (rpm) to radians per second (rad/s):
- There are 2π radians in one revolution.
- Divide the rpm by 60 to convert it to rotations per second.
- Multiply the rotations per second by 2π to convert it to radians per second.
In this case:
Angular speed = (600 rpm / 60) * 2π = 20π rad/s
Therefore, the angular speed at any point on the wheel is 20π rad/s.
To compute the tangential speed at a distance of 0.5 meters from the center of the wheel, we can use the formula:
Tangential speed = Radius * Angular speed
2. Plug in the values:
- The radius (r) is 0.5 meters.
- The angular speed (ω) is 20π rad/s.
Tangential speed = 0.5 meters * 20π rad/s
Therefore, the tangential speed 0.5 meters from the center of the wheel is 10π meters per second (m/s).