Frictionless half-pipe and rotational motion question

Thread starter AJDangles
Start date Jan 4, 2012
Tags

Frictionless Motion Rotational Rotational motion

In summary, the conversation discusses a problem involving a block sliding down a frictionless half-pipe and determining its velocity, tangential acceleration, radial acceleration, and angular acceleration at various angular displacements. The conversation covers the use of rotational motion equations, converting degrees to radians, using energy conservation, and finding the height as a function of angle in order to solve for the tangential velocity. Further discussion includes the use of trigonometry to solve for the angular acceleration and the formula for tangential acceleration. The conversation concludes with a question about attending McMaster University.

Jan 6, 2012

AJDangles

Doc Al said:

All you're doing is applying Newton's 2nd law in the tangential direction. For the tangential forces (the x-direction), the only force is the x-component of the weight. So:
ƩF_x = ma_x
mg cosθ = ma_x

So... a_x = g cosθ

Let me know if this gets at your question. If not, ask again.

Ok... I think I get it now. Thanks a lot. Just one more picture to make sure my triangle is in the right spot:

<h2>1. What is a frictionless half-pipe?</h2><p>A frictionless half-pipe is a curved surface, typically made of metal or plastic, that is completely smooth and has no friction. This means that when an object, such as a skateboard, is placed on the half-pipe, it will not experience any resistance or slowing down due to friction.</p><h2>2. How does a frictionless half-pipe affect rotational motion?</h2><p>A frictionless half-pipe allows for a more ideal or perfect rotational motion. This means that the object will continue to rotate without any external forces acting upon it, such as friction or air resistance. This allows for a more accurate study of rotational motion and its principles.</p><h2>3. What is the significance of studying rotational motion on a frictionless half-pipe?</h2><p>Studying rotational motion on a frictionless half-pipe allows for a better understanding of the fundamental principles of rotational motion. By eliminating the effects of friction, scientists can focus on the effects of other factors, such as mass, velocity, and angular acceleration, on the object's rotation.</p><h2>4. How is a frictionless half-pipe used in scientific experiments?</h2><p>A frictionless half-pipe is often used in experiments to study rotational motion and its principles. Scientists may use it to observe the effects of different factors, such as changing the object's mass or velocity, on its rotation. It can also be used to demonstrate the conservation of angular momentum and other laws of rotational motion.</p><h2>5. Are there any real-life applications of a frictionless half-pipe?</h2><p>While a completely frictionless surface is not possible in the real world, the concept of a frictionless half-pipe can be applied to various real-life situations. For example, in sports such as skateboarding and snowboarding, athletes often perform tricks and maneuvers on half-pipes that are designed to minimize friction and allow for smoother and more consistent rotations.</p>

1. What is a frictionless half-pipe?

A frictionless half-pipe is a curved surface, typically made of metal or plastic, that is completely smooth and has no friction. This means that when an object, such as a skateboard, is placed on the half-pipe, it will not experience any resistance or slowing down due to friction.

2. How does a frictionless half-pipe affect rotational motion?

A frictionless half-pipe allows for a more ideal or perfect rotational motion. This means that the object will continue to rotate without any external forces acting upon it, such as friction or air resistance. This allows for a more accurate study of rotational motion and its principles.

3. What is the significance of studying rotational motion on a frictionless half-pipe?

Studying rotational motion on a frictionless half-pipe allows for a better understanding of the fundamental principles of rotational motion. By eliminating the effects of friction, scientists can focus on the effects of other factors, such as mass, velocity, and angular acceleration, on the object's rotation.

4. How is a frictionless half-pipe used in scientific experiments?

A frictionless half-pipe is often used in experiments to study rotational motion and its principles. Scientists may use it to observe the effects of different factors, such as changing the object's mass or velocity, on its rotation. It can also be used to demonstrate the conservation of angular momentum and other laws of rotational motion.

5. Are there any real-life applications of a frictionless half-pipe?

While a completely frictionless surface is not possible in the real world, the concept of a frictionless half-pipe can be applied to various real-life situations. For example, in sports such as skateboarding and snowboarding, athletes often perform tricks and maneuvers on half-pipes that are designed to minimize friction and allow for smoother and more consistent rotations.