Rotational motion problems involving radians

In summary, the conversation discusses an exam preview and a specific problem involving rotational and translational energy. The questioner is unsure about the application of a 90 degree angle and considers possibilities such as torque, work, and friction force. Another idea for a rotational problem is suggested.
  • #1
lorkp
1
0

Homework Statement


The professor gives us an exam preview where he hints at the types of problems via the picture. Attached is the preview. I have a question about pictures 1 and 2. It's probably a problem that involves rotational and translational energy, conservation of energy. If it's rolling without slipping, it would mean a torque problem. What's throwing me off, however, is that he shows that there's a 90 degree angle. But I don't have a concrete reason for why it's applicable. It could do with radians traveled and so it could be a work problem because work = torque * delta theta. However the friction force that provides the torque would be changing because the normal force would be changing, correct? I'm not sure how to account for that.

Any other ideas for a rotational problem that would involve radians?

Thank you


Homework Equations





The Attempt at a Solution

 

Attachments

  • FEpreview-1.pdf
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  • #2
welcome to pf!

hi lorkp! welcome to pf! :smile:
lorkp said:
… What's throwing me off, however, is that he shows that there's a 90 degree angle.

he's simply telling you that the initial angle is 45° (or 135°)

anwyay, since it looks as if the ball is going to be gently nudged into the arc, it looks to me like an shm question :wink:
 

1. What is rotational motion in radians?

Rotational motion in radians is a way of measuring angles in a circular motion. It is based on the concept of using the radius of a circle as the unit of measurement. One radian is equal to the length of the radius along the circumference of a circle.

2. How do I convert degrees to radians?

To convert degrees to radians, you can use the formula: radians = (degrees * π) / 180. Simply multiply the number of degrees by π (pi) and divide by 180 to get the equivalent value in radians.

3. What is the relationship between linear and angular velocity?

The relationship between linear and angular velocity is that they are directly proportional. This means that as the angular velocity increases, the linear velocity also increases. The exact relationship is given by the equation: linear velocity = radius x angular velocity.

4. How do I calculate the arc length in radians?

To calculate the arc length in radians, you can use the formula: arc length = radius x angle in radians. This means that the arc length is equal to the radius of the circle multiplied by the angle in radians.

5. Can I use radians in rotational motion problems with non-circular motion?

Yes, radians can be used in rotational motion problems involving any type of motion, not just circular motion. This is because radians are a unit of measurement for angles, and can be applied to any type of rotation, whether it is circular or non-circular.

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