Angular Speed
The angular speed of an object is defined as the rate at which it rotates or moves around a central point. It is measured in radians per second (rad/s). In this case, the stone is swung in a horizontal circle on a 2m chord with a time period of 1s. To find the angular speed, we need to determine the angle through which the stone travels in one second.

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, the radius is half of the chord length, so r = 1m. Therefore, the circumference is C = 2π(1) = 2πm.

The time period T is the time taken for one complete revolution or one trip around the circle. In this case, T = 1s.

To find the angle through which the stone travels in one second, we can use the formula θ = 2π/T. Substituting the values, we have θ = 2π/1 = 2π rad.

The angular speed (ω) is defined as the change in angle per unit time. Therefore, ω = θ/T. Substituting the values, we have ω = 2π/1 = 2π rad/s. Hence, the angular speed of the stone is 2π rad/s.

Radial Acceleration
The radial acceleration of an object moving in a circular path is the acceleration towards the center of the circle. It is directed along the radius of the circle and can be determined using the formula a = v^2/r, where v is the linear velocity and r is the radius of the circle.

In this case, the stone is swung with a constant speed, which means the magnitude of the linear velocity is constant. As the stone moves in a horizontal circle, the linear velocity is tangent to the circle at each point. The radial acceleration is responsible for changing the direction of the velocity vector at each point.

Since the stone is swung on a 2m chord, the radius of the circle is 1m (half of the chord length). Let's assume the linear velocity of the stone is v.

The radial acceleration (a) can be determined using the formula a = v^2/r. In this case, a = v^2/1 = v^2 m/s^2.

Therefore, the radial acceleration of the stone depends on the square of the linear velocity and is inversely proportional to the radius of the circle. The exact value of the radial acceleration cannot be determined without knowing the velocity, but we can conclude that it increases as the velocity increases and decreases as the radius increases.

3.14