Rolling motion of a rigid body problem

In summary, the question is asking for the amount of work required to get a solid sphere with a radius of 0.200 m and a mass of 150 kg rolling with an angular speed of 50.0 rad/s on a horizontal surface. Your attempt at solving the problem involved finding the velocity of the sphere and then calculating the centripetal force and work. However, you did not take into account the rotational kinetic energy of the sphere, which is necessary to fully solve the problem. The correct answer that the teacher gave was 10500 J, which takes into account both the rotational and translational kinetic energy.
  • #1
Minchi
2
0
1. A solid sphere has a radius of 0.200 m and a mass of 150 kg. How much work is required to get the sphere rolling with an angular speed of 50.0 rad/s on a horizontal surface? Assume the sphere starts from rest and rolls without slipping

2. The attempt at a solution

I found V first.

V= rw
= 0.2 x 50
=10 m/s

Then Fc

Fc = mv^2/r
= (150)(10)^2 / 0.2
=75000 N

W= F X R
= 75000 x 0.2
= 15000 J

The answer the teacher gave was 1.05 x 10^4 J or 10500 J...

What did I do wrong?

Thank you for your help!
 
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  • #2
Minchi said:
1. A solid sphere has a radius of 0.200 m and a mass of 150 kg. How much work is required to get the sphere rolling with an angular speed of 50.0 rad/s on a horizontal surface? Assume the sphere starts from rest and rolls without slipping

2. The attempt at a solution

I found V first.

V= rw
= 0.2 x 50
=10 m/s

Then Fc

Fc = mv^2/r
= (150)(10)^2 / 0.2
=75000 N

W= F X R
= 75000 x 0.2
= 15000 J
This is the rotational energy. In addition to just spinning in place the sphere is moving forward. You have to take the translational kinetic energy into account too.

The answer the teacher gave was 1.05 x 10^4 J or 10500 J...

What did I do wrong?

Thank you for your help!
 
  • #3
I = mi ri^2
=(150)(0.2)^2
= 6 kg m2

KE= 1/2 I w^2
=(0.5)(6)(50)^2
=7500 J

um...where do I fit this into what I did above?

Was all my steps above required to the question?
 

FAQ: Rolling motion of a rigid body problem

1. What is rolling motion of a rigid body?

Rolling motion of a rigid body refers to the movement of an object (rigid body) in which it rotates and translates simultaneously without slipping. This type of motion is commonly observed in objects such as wheels and balls.

2. What is the difference between rolling motion and sliding motion?

While both types of motion involve the movement of an object, the main difference is in the contact between the object and the surface it is moving on. In rolling motion, there is no slipping between the object and the surface, whereas in sliding motion, there is.

3. What factors affect the rolling motion of a rigid body?

The rolling motion of a rigid body is affected by several factors, including the shape and size of the object, the surface it is rolling on, and any external forces acting on the object. Additionally, the moment of inertia and angular velocity of the object also play a role in its rolling motion.

4. How is the rolling motion of a rigid body calculated?

The rolling motion of a rigid body can be calculated using the rotational kinematics equations, which relate the angular velocity and angular acceleration of the object to its linear velocity and linear acceleration. The moment of inertia and external forces must also be taken into account in the calculations.

5. What are some real-world applications of rolling motion of a rigid body?

Rolling motion of a rigid body is commonly used in various machines and vehicles, such as cars, bicycles, and conveyor belts. It is also important in sports, such as bowling, golf, and basketball, where balls are used and rolling motion is involved.

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