A stone is attached to the end of an elastic string and whirled round in a circle path of radius 80cm if the stone makes 9 complete revolution in 3 seconds .find its angular and linear velocities during this period
A stone is tied to a string is made to revolve in horizontal circle of radius 4m with an angular speed of 2 radian per seconds with what tangential velocity will the stone move off the circle if the string cuts
To find the angular and linear velocities of the stone, we need to use the formulas:
Angular velocity (ω) = (2 * π * N) / T
Linear velocity (v) = ω * r
Where:
- ω is the angular velocity in rad/s
- N is the number of revolutions
- T is the time in seconds
- v is the linear velocity in cm/s
- r is the radius in cm
Given that the stone makes 9 complete revolutions in 3 seconds and the radius is 80 cm, we can calculate:
1. Angular velocity:
ω = (2 * π * N) / T
= (2 * π * 9) / 3
= 6π rad/s
2. Linear velocity:
v = ω * r
= 6π * 80
= 480π cm/s
Therefore, the angular velocity is 6π rad/s and the linear velocity is 480π cm/s during this period.
velocity=distance/time=2PI*.8/3 *9
angular velociy=2PI/peiod= 9*2PI/3
linear velociyt= w*radius