A flywheel turns at 480rpm .find the tangential speed of a point on this flywheel at a distance of 30cmfrom its center.
480 rev/min * 30*2π cm/rev = 28800π cm/min
To find the tangential speed of a point on a rotating flywheel, you can use the formula:
Tangential speed = Radius × Angular speed
The angular speed is given in rotations per minute (rpm), so we need to convert it to radians per second:
1 rpm = 2π radians/60 seconds
Now, let's calculate the tangential speed:
1. Convert the angular speed to radians per second:
Angular speed = 480 rpm = (480 × 2π radians)/60 seconds
2. Calculate the tangential speed:
Tangential speed = Radius × Angular speed
= 30 cm × ((480 × 2π radians)/60 seconds)
3. Simplify the equation:
Tangential speed = 30 cm × (16π radians/second)
= 480π cm/second
Hence, the tangential speed of a point on the flywheel, 30 cm from its center, is 480π cm/second.
To find the tangential speed of a point on the flywheel at a distance of 30 cm from its center, we need to use the formula:
Tangential speed = Angular speed × Radius
1. Convert the given angular speed from revolutions per minute (rpm) to radians per second (rad/s).
- Since 1 revolution is equal to 2π radians, we can convert rpm to rad/s by multiplying by (2π/60).
- So, the angular speed in rad/s is: 480 rpm × (2π/60) = 480 × (2π/60) rad/s.
2. Substitute the angular speed and radius into the formula to find the tangential speed.
- The radius is given as 30 cm, which can be converted to meters by dividing by 100.
- Plug in the values: Tangential speed = (480 × 2π/60) rad/s × 0.3 m.
3. Calculate the tangential speed.
- Simplify and calculate: Tangential speed = (480 × 2π/60) rad/s × 0.3 m ≈ 30.159 m/s.
Therefore, the tangential speed of a point on the flywheel at a distance of 30 cm from its center is approximately 30.159 m/s.