A stone is attached to the end of an inelastic string and whirled in a circular path of radius 30cm if the stone makes nine complete oscillation in 3seconds find the angular velocity and linear velocity during the period
angular velocity is ω = 2πf = 2π/(3/9) = 6π
linear velocity v = rω = 6π * 30 = 180π cm/s
To find the angular velocity, we need to know the formula for angular velocity:
Angular velocity (ω) = (2π * number of oscillations) / time
In this case, the number of oscillations is 9 and the time is 3 seconds.
ω = (2π * 9) / 3
= 6π radians per second
Therefore, the angular velocity during this period is 6π radians per second.
To find the linear velocity, we can use the formula for linear velocity:
Linear velocity (v) = angular velocity (ω) * radius
In this case, the radius is given as 30 cm.
v = (6π) * 30
= 180π cm per second
Thus, the linear velocity during this period is 180π cm per second.
To find the angular velocity and linear velocity during the period, we can start by using the formula for angular velocity:
Angular velocity (ω) = 2πf
Where:
- ω is the angular velocity in radians per second
- π is a constant (approximately 3.14)
- f is the frequency in oscillations per second
In this case, the stone makes nine complete oscillations in 3 seconds. So, the frequency (f) can be calculated as:
f = 9 oscillations / 3 seconds = 3 oscillations per second
Substituting this value into the formula for angular velocity:
Angular velocity (ω) = 2π * 3 = 6π radians per second
Now, to find the linear velocity, we can use the formula:
Linear velocity (v) = ω * r
Where:
- v is the linear velocity
- ω is the angular velocity in radians per second
- r is the radius of the circular path
Given that the radius (r) is 30 cm, we need to convert it to meters (since the SI unit is meters). 1 cm = 0.01 meters, so:
r = 30 cm * 0.01 = 0.3 meters
Substituting the values into the linear velocity formula:
Linear velocity (v) = (6π radians per second) * (0.3 meters) ≈ 5.66 meters per second
Therefore, the angular velocity during the period is 6π radians per second, and the linear velocity during the period is approximately 5.66 meters per second.