An object of mass 0.50 kg on the end of a string is whirled round in a horizontal circle of radius 2.0m with a constant speed of 10m/s.Find its angular velocity and tension in the string( string is horizontal)answer should be 25.5 N

v = omega r

10 = omega(2)
omega = 5 radians/second

Ac = v^2/r = omega^2 r = 25*2 = 50 m/s^2

F = m a = .5 *50 = 25 N
(not 25.5)

To find the angular velocity and tension in the string, we can use the following steps:

Step 1: Determine the centripetal acceleration.
The centripetal acceleration is given by the formula:
a = v^2 / r

where:
a = centripetal acceleration
v = speed of the object
r = radius of the circle

In this case, the speed of the object is 10 m/s and the radius of the circle is 2.0 m.

Substituting the values into the formula, we get:
a = (10 m/s)^2 / 2.0 m
a = 100 m^2/s^2 / 2.0 m
a = 50 m/s^2

Step 2: Convert the centripetal acceleration to angular acceleration.
The angular acceleration is related to the centripetal acceleration by the formula:
a = r * alpha

where:
alpha = angular acceleration

In this case, the radius of the circle is 2.0 m and the centripetal acceleration is 50 m/s^2.

Substituting the values into the formula, we get:
50 m/s^2 = 2.0 m * alpha
alpha = 50 m/s^2 / 2.0 m
alpha = 25 rad/s^2

Step 3: Calculate the angular velocity.
The angular velocity is related to the angular acceleration by the formula:
alpha = delta(omega) / delta(t)

where:
omega = angular velocity
t = time

In this case, we are given that the speed is constant, which means the angular acceleration is zero. Therefore, the angular velocity is constant as well.

Hence, the angular velocity is 25 rad/s.

Step 4: Determine the tension in the string.
The tension in the string can be found using the formula for centripetal force:
F = m * a

where:
F = tension in the string
m = mass of the object
a = centripetal acceleration

In this case, the mass of the object is 0.50 kg and the centripetal acceleration is 50 m/s^2.

Substituting the values into the formula, we get:
F = 0.50 kg * 50 m/s^2
F = 25 N

Hence, the tension in the string is 25 N.