calculate , in newtons correct to the nearest unit, the force necessary to maintain a body of mass 2kg in uniform angular speed of 2rev/s in a circle of radius 0.2m
To calculate the force necessary to maintain a body in uniform angular speed in a circular motion, you can use the formula for centripetal force:
F = (m * v^2) / r,
where F is the force, m is the mass of the body, v is the linear velocity, and r is the radius of the circular path.
In this case, the mass (m) of the body is given as 2 kg, the angular speed (2 rev/s) needs to be converted to linear velocity, and the radius (r) is given as 0.2 m. Let's break it down step by step:
1. Convert angular speed to linear velocity:
The linear velocity (v) can be calculated by multiplying the angular speed by the circumference of the circular path. Since you are given the radius (0.2 m), the circumference will be 2 * π * r.
v = 2 rev/s * 2π * 0.2 m = 2 * 2π * 0.2 m/s.
2. Calculate the force:
Now that you have the linear velocity, you can substitute the values into the formula to find the force:
F = (m * v^2) / r
F = (2 kg) * ((2 * 2π * 0.2 m/s)^2) / 0.2 m.
Solving this equation will give you the force necessary to maintain the body in uniform angular speed in newtons.