you swing a 2.2 kg stone in a circle of radius 75 cm. At what speed should you swing it so its centripetal acceleration will be 9.8 m/s^2
a rad = V^2 / R now i know R = 75 cm what do I put for V^2
Your answer will likely be in radians, so you could be better off expressing the acceleration in angular velocity, ω, in radians per second.
a=V2/R
=ω2R
Since a and R are both known, you can go ahead and solve for ω.
To find the required speed, we can rearrange the formula for centripetal acceleration:
a_c = V^2 / R
Given that the centripetal acceleration (a_c) is 9.8 m/s^2 and the radius (R) is 75 cm, we need to find V^2.
First, let's convert the radius from centimeters to meters:
R = 75 cm = 0.75 m
Now substitute the known values into the centripetal acceleration formula:
9.8 m/s^2 = V^2 / 0.75 m
To solve for V^2, multiply both sides of the equation by 0.75 m:
V^2 = 9.8 m/s^2 * 0.75 m
V^2 = 7.35 m^2/s^2
Therefore, V^2 is equal to 7.35 m^2/s^2.