Rolling without slipping

In summary, the question is asking for the magnitude of the torque due to static friction acting on a rolling ball on an incline. The answer options include various combinations of the ball's mass, radius, and the magnitude of the friction force. The correct answer is rfsin theta, which takes into account the direction of the friction force and its angle with the radius. Friction cannot be ignored in this scenario, as without it the ball would slide instead of roll.
  • #1
raisatantuico
11
0

Homework Statement



a solid metal ball of mass M and radius R is rolling without slipping down and incline. A static friction force of magnitude f is acting on the ball. What is the magnitude of the torque due to static friction?
a.) zero b.) rfcos theta c.) rfsin theta d.)Rf e. MRF

Homework Equations



ki+ui=kf=uf (conservation of energy)

The Attempt at a Solution


since the ball is rolling without slipping, why is there friction involved? do we just simply ignore friction, so the answer will just be the definition of torque: rfsin theta ?
 
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  • #2
raisatantuico said:
since the ball is rolling without slipping, why is there friction involved?
Without friction, the ball would slide not roll.
do we just simply ignore friction, so the answer will just be the definition of torque: rfsin theta ?
No, you cannot ignore friction. (And how is that answer ignoring friction anyway? It includes f!)
 
  • #3
Doc Al said:
Without friction, the ball would slide not roll.

No, you cannot ignore friction. (And how is that answer ignoring friction anyway? It includes f!)

f in the equation is force. torque= radius x force sin theta. net torque is also equal to angular acceleration x moment of inertia

where does friction come in this defintion of torque?
 
  • #4
Here 'f' is the friction force. (What direction does friction act? What angle does it make with the radius?)
 
  • #5


I would like to clarify that even if the ball is rolling without slipping, there is still a static friction force acting on it. This is because the surface of the incline is exerting a normal force on the ball, causing the ball to experience a friction force in the opposite direction. This friction force is necessary to prevent the ball from slipping and to maintain its rolling motion.

Therefore, the magnitude of the torque due to static friction can be calculated using the equation τ = rfsinθ, where r is the radius of the ball, f is the magnitude of the static friction force, and θ is the angle between the radius vector and the direction of the friction force. This means that the correct answer is c.) rfsinθ.

Additionally, the conservation of energy equation mentioned in the problem can also be used to solve for the magnitude of the torque. Since the ball is rolling without slipping, there is no change in its kinetic energy, so the initial kinetic energy (due to its rolling motion) is equal to the final kinetic energy (due to its translational motion). This means that the initial kinetic energy can be expressed as 1/2Iω^2, where I is the moment of inertia of the ball and ω is its angular velocity. The final kinetic energy can be expressed as 1/2Mv^2, where M is the mass of the ball and v is its linear velocity. Equating these two expressions and solving for the angular velocity, we get ω = v/r. The torque can then be calculated as τ = Iα, where α is the angular acceleration of the ball. Since the ball is rolling without slipping, α = a/r, where a is the linear acceleration of the ball. Substituting these values into the torque equation, we get τ = Ia/r = Mra/r = Mrf, which is equivalent to c.) rfsinθ.

In conclusion, the correct answer is c.) rfsinθ, and the presence of friction in this scenario is necessary to maintain the ball's rolling motion without slipping.
 

1. What is rolling without slipping?

Rolling without slipping is a type of motion that occurs when an object, such as a wheel, moves forward without sliding or slipping at the point of contact with the ground. This means that the object is both rotating and translating at the same time.

2. How is rolling without slipping different from rolling with slipping?

In rolling without slipping, the point of contact between the object and the ground remains stationary, while in rolling with slipping, the point of contact moves. This is due to the presence of static friction, which provides a force that prevents slipping in rolling without slipping.

3. What are the conditions for rolling without slipping to occur?

The conditions for rolling without slipping are a combination of rotational and translational motion. The object must have a non-zero angular velocity and a non-zero linear velocity, and the point of contact must have zero velocity. In addition, the coefficient of static friction between the object and the ground must be greater than or equal to the ratio of the object's linear velocity to its angular velocity.

4. What are some real-world examples of rolling without slipping?

Some common examples of rolling without slipping include a car driving down the road, a bicycle moving forward, and a ball rolling down a ramp. In all of these cases, the object is both rotating and translating, and there is no slipping at the point of contact with the ground.

5. How is rolling without slipping important in physics and engineering?

Rolling without slipping is important in physics and engineering because it allows for efficient and controlled motion. It is also a fundamental concept in the study of rotational motion and is used in the design and analysis of various mechanical systems, such as gears and wheels.

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