Rotational Motion of an object

In summary, the first problem involves finding the tension in a string when a 0.400-kg object is swung in a circular path with an angular speed of 8.00 rad/s. The second problem involves finding the angle at which a curve with a radius of 52 m should be banked for a car traveling at 12 m/s with no friction needed to prevent slipping.
  • #1
todd.debacker
2
0
I have two problems I am working on, and I have no idea about either

Homework Statement



1. A 0.400-kg object is swung in a circular path and in a vertical plane on a 0.500-m-length string. If the angular speed at the bottom is 8.00rad/s, what is the tension in the string when the object is at the bottom of the circle?


2. At what angle (relative to the horizontal) should a curve 52 m in radius be banked if no friction is required to prevent the car from slipping when traveling at 12 m/s? (g-9.8m/s^2)


Homework Equations




1 . m(v^2/r)=T ??

2. ?


The Attempt at a Solution



?
 
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  • #2
Well, for the first problem, you'll need to relate the objects tangential speed to its angular speed. Any idea on what equation you should use? (Hint: We're dealing with circular motion).
 
  • #3
I have been attempting to use Vt=rw and then plugging that number into m(v^2/r) to give me the total force

Is the tension the only force?
 
  • #4
The tension is not the only force, but it's the only force we're concerned with. If you mean "Vt" to be the tangential velocity, that's the correct equation.
 

1. What is rotational motion?

Rotational motion refers to the movement of an object around an axis or center point. This type of motion is circular or curved in nature and can be seen in objects such as planets orbiting around the sun or a spinning top.

2. How is rotational motion different from linear motion?

Rotational motion involves movement around an axis, while linear motion involves movement in a straight line. In rotational motion, the distance traveled by each point on the object is different, while in linear motion, the distance traveled by each point is the same.

3. What is angular velocity?

Angular velocity is a measure of how fast an object is rotating around an axis. It is defined as the change in angular displacement over time and is typically measured in radians per second.

4. How is rotational motion related to torque?

Torque is the rotational equivalent of force, and it is what causes rotational motion. It is a measure of the force applied to an object at a certain distance from the axis of rotation. The greater the torque, the greater the rotational motion of an object.

5. What are some real-world examples of rotational motion?

Some examples of rotational motion in everyday life include the rotation of tires on a car, the spinning of a ceiling fan, and the rotation of a merry-go-round at a playground. Other examples include the rotation of the Earth on its axis and the rotation of a wind turbine blade.

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