How Does Friction Affect Wheel Motion on a Horizontal Surface?

In summary, a wheel with a mass of 10 kg and a radius of 0.3 m is rolling smoothly on a horizontal surface with a constant horizontal force of 10 N. The acceleration of its center of mass is 0.6 m/s^2. To find the frictional force in unit-vector notation, the equation (10N) = f - (10kg)(9.8m/s^2)sin0* = (10kg)(0.6 m/s^2) should be used, resulting in f = (-4.00 N)i. For part b, the rotational inertia of the wheel about its center of mass is found by using the equation (-4 N)(0.3m) =
  • #1
kara
54
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The question is:

A wheel is rolling smoothly on horizontal surface. There is a constant horizontal force of magnitude 10 N. Wheel has mass of 10 kg, and radius of 0.3 m. The accel. of its centre of mass has mag. of 0.6 m/s^2.

I am asked to find frictional force in unit-vector notation. This is what i did:
(10N) = f - (10kg)(9.8m/s^2)sin0* = (10kg)(0.6 m/s^2)
(10N)-f = 6.0
-f = -4.0

Since there is clockwise angluar acccel the friction is a negative value. So my answer is f = (-4.00 N)i

For part b it asks for the rotational inertia of the wheel about its centre of mass. This is what I've done so far:

(-4 N)(0.3m) = I (-0.6m/s^2/0.3m)
-1.20 = I(-2)
I = 0.600 rad/s

Am i on the right track?? Please help!
 
Last edited:
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  • #2
Friction tends to retard the motion, and I assume the applied force and the acceleration are in one direction, with friction in the opposite direction. Your positive answer for f is because you have it in the wrong place in your equation for it to be negative. If you wrote F + f = ma, then f would be found to be negative. Your result for I has the wrong dimensions.
 
  • #3


Yes, you are on the right track. Your calculation for the frictional force in unit-vector notation is correct. The negative value indicates that the frictional force is acting in the opposite direction of the horizontal force, which makes sense since the wheel is rolling in the direction of the horizontal force.

For part b, you are correct in using the formula I = τ/α to calculate the rotational inertia. However, there are a few errors in your calculation. First, the unit of rotational inertia is kg*m^2, not rad/s. So the correct unit for the left side of the equation would be kg*m^2. Second, the value of α that you used is incorrect. The correct value of α in this case is 0.6 m/s^2, which is the acceleration of the center of mass. Finally, the unit of τ in this equation is N*m, not N. So the correct unit for the right side of the equation would be N*m. Putting all of this together, the correct equation is:

-4 N * 0.3 m = I * (0.6 m/s^2 / 0.3 m)
-1.2 N*m = I * 2 N
I = 0.6 kg*m^2

So the rotational inertia of the wheel about its center of mass is 0.6 kg*m^2. This means that it would take a torque of 0.6 N*m to produce an angular acceleration of 1 rad/s^2.
 

What is rolling resistance?

Rolling resistance is the force that opposes the movement of a rolling object, such as a wheel or ball, on a surface. It is caused by the deformation of the object and the friction between the object and the surface.

How does the weight of an object affect its rolling speed?

The weight of an object does not affect its rolling speed. This is because the force of gravity acting on the object is balanced out by the normal force from the surface, resulting in a net force of zero. Rolling speed is primarily determined by the shape and material of the object, as well as the surface it is rolling on.

What is the difference between rolling and sliding friction?

Rolling friction is the force that opposes the rotation of a rolling object, while sliding friction is the force that opposes the sliding motion of an object on a surface. Rolling friction is typically much less than sliding friction, making it more energy efficient for objects to roll rather than slide.

How does the shape of an object affect its rolling resistance?

The shape of an object can greatly affect its rolling resistance. Objects with a larger surface area in contact with the ground, such as a flat tire, will have higher rolling resistance than objects with a smaller surface area, like a round wheel. This is due to the increased friction between the object and the surface.

What role does air resistance play in rolling objects?

Air resistance, also known as drag, can greatly affect the rolling speed of an object. Objects with a larger surface area, such as a ball with ridges, will experience more air resistance and therefore have a slower rolling speed compared to objects with a smoother surface. Air resistance can also cause objects to lose energy and slow down over time.

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