a stone is attached to the end of an inelastic string and whirled in a circular path of radius of 30cm if the stone makes 9complete revolution in 3 seconds find the angular and linear velocities during the period
To find the angular velocity, we need to find the angle covered by the stone in the given time period.
Given:
- Radius of the circular path (r) = 30 cm
- Number of complete revolutions made by the stone (n) = 9
- Time taken for the given revolutions (t) = 3 seconds
First, we need to find the angle covered by the stone in radians:
- We know that 1 revolution is equal to 2π radians.
- So, the angle covered by the stone in 9 revolutions = 9 * (2π) radians.
- Therefore, the angle covered by the stone in the given time period = (9 * 2π) / t radians.
Next, we can find the angular velocity by dividing the angle covered by the time taken:
- Angular velocity (ω) = Angle covered / Time taken.
- Therefore, angular velocity (ω) = [(9 * 2π) / t] radians/second.
To find the linear velocity, we can multiply the angular velocity by the radius of the circular path:
- Linear velocity (v) = Angular velocity (ω) * Radius (r).
- Therefore, linear velocity (v) = [(9 * 2π) / t] * 30 cm/second.
Now, we can calculate the values by substituting the given values into the equations.
Period: 3/9= .333sec
angular velocity=2PI/.333 rad/sec
linear veloicty=.3*2pi/.333 m/s