Rotational Motion (Inclined Plane)

In summary, the question is about which object, a solid cylinder or a solid sphere, would reach the ground first when placed on an inclined plane. The sphere would reach the ground first due to its mass distribution, but the question asks how to show this mathematically. The suggestion is to use energy methods and calculate the kinetic energy of the cylinder and sphere at the bottom of the plane to determine which has a greater velocity. This can be done using the formula mgh=1/2mv^2(1+k^2/r^2), where k is the radius of gyration. The person asking the question has figured it out and the conversation mentions AP Physics C as a potential course.
  • #1
Izzybee
11
0
[SOLVED] Rotational Motion (Inclined Plane)

Hi Everyone!
My question is: A solid cylinder and a solid sphere are resting on top of a inclined plane. Using mathematics, which object would reach the ground first. Given: I (cylinder) = 1/2mr ^2 and I (sphere) = 2/5 mr ^2.

I know that the sphere would reach the ground first because of its mass distribution, but I am not quite sure how to show it mathematically. My teacher said a problem like this will show up on my test Monday!

Please help!
 
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  • #2
What is the energy of a rotating solid?
 
  • #3
I think what kurdt's suggesting is to try using energy methods.

p.s. Are you taking AP Physics C?
 
  • #4
CALCULATE THE KINETIC ENERGY OF THE CYLINDER AND THE SPHERE AT THE BOTTOM OF THE PLANE...AND THEN FIND WHICH OF THE TWO HAS THE GREATER VELOCITY...

THE ONE WITH GREATER VELOCITY IS THE ONE WHICH COMES DOWN EARLY..

USE THE FORMULA..

mgh=1/2mv^2(1+k^2/r^2)

K(RADIUS OF GYRATION)==I/M
 
  • #5
Thanks, but I figured it out!
P.S: What is AP Physics C??
 
  • #6
Advanced Placement college board course. Its an American thing I believe.
 
  • #7
No I am not.
 

1. What is rotational motion on an inclined plane?

Rotational motion on an inclined plane is the movement of an object that is both rotating and sliding down an inclined surface.

2. How is rotational motion calculated on an inclined plane?

The rotational motion on an inclined plane is calculated using the principles of torque and angular acceleration. The torque is calculated as the product of the force and the distance from the pivot point, while the angular acceleration is calculated as the ratio of the torque to the moment of inertia of the object.

3. What factors affect rotational motion on an inclined plane?

The factors that affect rotational motion on an inclined plane include the angle of the incline, the mass and shape of the object, and the coefficient of friction between the object and the inclined surface.

4. What is the difference between rotational and translational motion on an inclined plane?

Rotational motion involves the rotation of an object around an axis, while translational motion involves the movement of an object in a straight line. On an inclined plane, both rotational and translational motion can occur simultaneously.

5. How does rotational motion on an inclined plane relate to real-life situations?

Rotational motion on an inclined plane is commonly seen in everyday life, such as in the movement of a rolling ball on a ramp or the motion of a spinning top on an inclined surface. It is also used in engineering and physics to analyze the movement of various objects and design machines and structures.

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