Acceleration of center of mass

In summary, the acceleration of the sphere's center of mass down the inclined plane is gsinX, and there are three forces acting on the sphere: force of friction, normal force, and force of gravity. To solve for the acceleration, Newton's 2nd law for both translation and rotation must be applied. The sphere rolls without slipping, completing one revolution while going a distance of 2\pi R along the incline.
  • #1
UrbanXrisis
1,196
1
A solid shere of mass M and radius R rolls without slipping down an inclined plane whose incline angle with the horizontal is 30 degrees. What is the acceleration of the sphere's center of mass?

gsinX is the acceleration, so it would be g/2 right?
 
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  • #2
No. While [itex]mg \sin \theta[/itex] is the component of the ball's weight along the incline, it is not the only force acting on the ball.
 
  • #3
A solid shere of mass M and radius R rolls without slipping down an inclined plane whose incline angle with the horizontal is 30 degrees.
 
  • #4
still not sure what you mean... so it doesn't slip, so what?
 
  • #5
Start by identifying all the forces acting on the sphere. (Hint: I count 3)
 
  • #6
force of friction, normal force, and force of gravity
 
  • #7
Right. To solve for the acceleration, you'll need to apply Newton's 2nd law for both translation and rotation.
 
  • #8
The point of "rolling without slipping" is that the sphere makes on complete revolution while going a distance [itex]2\pi R[/itex]
 

What is acceleration of center of mass?

Acceleration of center of mass is the rate of change of the velocity of a system's center of mass. It is a measure of how quickly the center of mass is speeding up or slowing down, regardless of its direction of motion.

How is acceleration of center of mass calculated?

Acceleration of center of mass is calculated by dividing the net force acting on a system by its total mass. This is represented by the equation a = F/m, where a is acceleration, F is net force, and m is mass.

What factors can affect the acceleration of center of mass?

The acceleration of center of mass is affected by the forces acting on the system, as well as the total mass of the system. Other factors such as friction, air resistance, and external forces can also impact the acceleration of center of mass.

What are some real-life examples of acceleration of center of mass?

Examples of acceleration of center of mass can be seen in various sports, such as throwing a javelin or shot put, where the athlete's body serves as the system and their center of mass is accelerated by the forces exerted on the object they are throwing. Another example is a rocket launch, where the acceleration of the rocket's center of mass is crucial for achieving liftoff.

How does acceleration of center of mass relate to Newton's laws of motion?

Acceleration of center of mass is directly related to Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. It also indirectly relates to Newton's first law of motion, as a system's center of mass will remain at a constant velocity unless acted upon by a net force.

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