A small 700 g ball on the end of a thin, light rod is rotated in a horizontal circle of radius 1.5 m. Calculate the torque needed to keep the ball rotating at a constant angular speed if the air resistance experienced by the ball is 0.1200 N. Ignore the rods moment of inertia and air resistance. Hint: Treat the small ball as a particle.
Torque = .12 * 1.5 Newton meters
There is no tangential acceleration so no one cares about the mass.
To determine the torque needed to keep the ball rotating at a constant angular speed, we first need to understand the concept of torque and its relation to angular speed and moment of inertia.
Torque is a rotational force that causes an object to rotate around an axis. It is calculated by multiplying the force applied perpendicular to the axis of rotation by the distance from the axis at which the force is applied.
In this case, we can treat the small ball as a particle since we are ignoring the rod's moment of inertia and air resistance. Therefore, the torque exerted on the ball can be determined using the equation:
Torque = Force * Radius
where Force is the net force acting on the ball and Radius is the radius of the circular path.
Given that the air resistance experienced by the ball is 0.1200 N, we can consider this as the net force acting on the ball since there are no other forces mentioned.
Now, let's calculate the torque:
Torque = Force * Radius
= 0.1200 N * 1.5 m
= 0.180 N ∙ m
Therefore, the torque needed to keep the ball rotating at a constant angular speed in this scenario is 0.180 N ∙ m.