A stone tied to a string is made to revolve in a horizontal circle of radius 4m with an angular speed of 2 radians per second .with what tangential velocity will the stone move off the circle if the string cuts?
v = rω = 4*2 m/s
To find the tangential velocity when the string cuts, you need to use the concept of centripetal acceleration and the formula for tangential velocity.
First, let's find the centripetal acceleration (ac):
The formula for centripetal acceleration is ac = ω^2 * r,
where ω is the angular speed in radians per second,
and r is the radius of the circle.
Given:
ω = 2 radians per second,
r = 4 meters.
Substituting these values into the formula, we have:
ac = (2^2) * 4
ac = 4 * 4
ac = 16 m/s^2
Next, we can use the formula for tangential velocity (v) to find the velocity at which the stone moves off the circle when the string is cut:
The formula for tangential velocity is v = ω * r,
where ω is the angular speed in radians per second,
and r is the radius of the circle.
Given:
ω = 2 radians per second,
r = 4 meters.
Substituting these values into the formula, we have:
v = 2 * 4
v = 8 m/s
Therefore, when the string is cut, the stone will move off the circle with a tangential velocity of 8 m/s.
To determine the tangential velocity at which the stone will move off the circle when the string is cut, we can use the concept of centripetal acceleration.
The centripetal acceleration is given by the formula:
a = r * ω²
Where:
a is the centripetal acceleration,
r is the radius of the circle, and
ω is the angular speed.
In this case, the radius of the circle is 4m and the angular speed is 2 radians per second.
a = 4m * (2 rad/s)²
a = 4m * 4 rad²/s²
a = 16m/s²
Now, to find the tangential velocity at which the stone moves off the circle, we can use the equation:
v = √(a * r)
Where:
v is the tangential velocity,
a is the centripetal acceleration, and
r is the radius of the circle.
v = √(16m/s² * 4m)
v = √(64m²/s²)
v = 8m/s
Therefore, the tangential velocity at which the stone will move off the circle when the string is cut is 8m/s.
V=2
r=4
W=x
2=4x
x=2/4
=1/2