A girl on a merry-go-round platform holds a pendulum in her hand. The pendulum is 6.0 m fr...

The angle of the pendulum can be calculated by considering the tension force on the pendulum. By resolving the tension force into the horizontal and the vertical components and equating horizontal component to the centripetal force acting on the pendulum and vertical component to the gravitational force acting on the pendulum in a downward direction. By using these equations, we finally calculate the angle of the pendulum.

SKETCH:

The sketch for the given problem is shown in the below figure.

RESEARCH:

Let ‘’ be the tensional force on the cable of the pendulum, then from the above diagram, the horizontal component of the tension will be equal to the centripetal force. Hence, the horizontal component of tension

…… (1)

Here and are the mass and linear speed of the pendulum and is the distance from the rotational axis to the pendulum.

The vertical upward component of the tension force is balanced by the weight of the pendulum.

…… (2)

Here is the acceleration due to gravity.

The relation between the angular and linear speeds is given by the equation

Here is the angular speed of the pendulum.

RESEARCH:

Now dividing the equation (1), by equation (2), we get

…… (3)

Given data:

The rotational speed of the platform,

The distance from the rotational axis to the pendulum,

The acceleration due to gravity,

CALCULATE

Substituting the values in the equation (3), we get the angle of the pendulum