Question

A rock attached to a string moves clockwise in uniform circular motion. In which direction from point $A$ is the rock thrown off when the string is cut? a) centrifugal b) normal c) gravity d) tension

Short answer

Answer: The rock moves in a direction tangent to the circular path at the point where the string is cut.

Step-by-step solution

Identify the forces acting on the rock

First, we need to identify the forces present when the rock is in uniform circular motion. There are two main forces acting on the rock: 1. Tension force, provided by the string pulling the rock inwards. 2. Centripetal force, needed to keep the rock in a circular path. Additionally, gravity acts on the rock, pulling it downwards.

Understand the effect of cutting the string

When the string is cut, the tension force acting on the rock disappears. However, the rock still has a tangential velocity at that instant, which means it will continue to move in a direction tangent to the circular path. This tangential velocity is caused by the centripetal force, which was keeping the rock in a circular motion.

Determine the direction of the tangent

To find the direction in which the rock is thrown off, we need to identify the direction of the tangent to the circular path at point $A$. Since the rock is moving clockwise in the circular path, the tangent at this point will be in a direction perpendicular to the radius vector and to the right.

Compare the given options with the tangent direction

Now, we should compare the tangent direction with the given options: a) Centrifugal force does not exist; it is a fictitious outward force, so this option can be discarded. b) Normal force is the force exerted by a surface perpendicular to the object. There is no surface involved in this case, so this option is not correct. c) Gravity acts downwards and has no direct influence on the rock's tangent direction, so this option is also incorrect. d) Tension force was acting inwards and has disappeared when the string was cut, so this option is not correct. None of the given options match the direction of the tangent. This seems to be a mistake in the given options. The correct answer should be: the rock is thrown off in a direction tangent to the circular path at point $A$.

Key concepts

Centripetal Force

Centripetal force is essential in understanding how objects move in a circular path. It is the force directed toward the center of a circle that keeps an object moving in a circular motion. Unlike other forces, it is not a separate force but generally arises from other forces like tension, gravity, or friction.

In the case of a rock attached to a string in circular motion, centripetal force ensures that the rock keeps moving along the circle. Without a sufficient centripetal force, the rock would fly off tangentially to the circle's path. Since the string tension in the exercise provides the necessary force, it aligns with the center of rotation.

It’s important to note that centripetal force is always directed towards the center while the object moves tangentially. When the string holding the rock breaks, the centripetal force vanishes, and the rock follows its instantaneous tangential velocity.

Tension Force

In a system like the rock on a string, the tension force plays a crucial role by providing the inward pull necessary for the centripetal force. Imagine you’re swinging a rock around in a circle using a string; the tension is the force you feel pulling against your hand, keeping the rock moving in a circle.

Tension is directed along the length of the string, pulling the rock towards the center of the circle. As soon as the string is cut or breaks, this tension force disappears, and the rock no longer feels the inward pull needed to maintain its circular path.

The loss of tension means the centripetal force is gone, explained in the exercise as why the rock then moves in a straight line tangent to the circle at the moment of release. It's a great example of real-life physics, emphasizing tension's impact on circular motion.

Tangential Velocity

Tangential velocity describes the motion of an object moving along the edge of a circle. This velocity is always tangent to the circle and is perpendicular to the radius at any given point of an object’s path.

Think about a race track; as you take a turn, your direction changes continuously, and at every point, your forward movement is straight, aligning with the tangent. This is similar to the rock problem; tangential velocity is what governs the direction of the rock when it’s released from circular motion.

The exercise highlights when the string is cut, the rock continued to move in a straight line. Its path is determined by its tangential velocity, which was set during its circular motion. Understanding tangential velocity helps us predict this motion and is fundamental for anything involving circular dynamics.