A stone is moved round a horizontal circle with a 20 cm long string tied to it. if centrepetal acceleration is 9.8 m/s2, then its angular velocity
v^2 = .20 m * 9.8 m/s^2
this is the tangential velocity (v)
divide by the radius to find angular
To find the angular velocity of the stone, we can use the formula for centripetal acceleration.
The centripetal acceleration is given by the equation:
a = (v^2) / r
Where:
a = centripetal acceleration, given as 9.8 m/s^2
v = velocity
r = radius
In this case, the radius (r) is given as 20 cm, which is equal to 0.2 meters.
We need to rearrange the equation to solve for velocity (v):
v^2 = a * r
Substituting the given values, we have:
v^2 = 9.8 m/s^2 * 0.2 m
Now, we can solve for v:
v^2 = 1.96 m^2/s^2
Taking the square root of both sides gives us:
v ≈ √1.96 ≈ 1.4 m/s
The final step is to calculate the angular velocity (ω), which is defined as the ratio of the linear velocity (v) to the radius (r):
ω = v / r
Substituting the values, we have:
ω = 1.4 m/s / 0.2 m
ω ≈ 7 rad/s
Therefore, the angular velocity of the stone is approximately 7 rad/s.