Calculating Angular Acceleration with Friction on an Inclined Plane

In summary, the problem involves a solid uniform cylinder with a mass of 5 kg being pulled up a 30 degree incline with a constant force of 45 Newtons parallel to the incline. The question is asking for the angular acceleration of the cylinder. The moment of inertia can be calculated using either (.5mr^2) or (.5mr^2 + mr^2), depending on the axis of rotation chosen. The friction force is the only force causing torque in this scenario, and its direction can be determined by considering which way the surfaces would slip without friction. It is recommended to use the center of mass of the cylinder as the axis of rotation for better understanding of the problem.
  • #1
ripper9100
7
0

Homework Statement


A solid uniform cylinder with mass 5 kg is being pulled with a constant force of 45 Newtons up a 30 degree incline. The force is acting on the cylinders center and is parallel to the incline. What is its angular acceleration?

I have a good idea on how to do the problem by using Newtons second law for a rigid body. The only part I'm confused about is on what the moment of inertia should be. I think Its either (.5mr^2) or (.5mr^2 +mr^2)?

please help
 
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  • #3
im also iffy on the net Torque. I am thinking that friction is the only force causing torque since the 45 N force is acting on the cylinders center.
am i right?
 
  • #4
Yes. I agree.
 
  • #5
thanks for the help
 
  • #6
ripper9100 said:
I have a good idea on how to do the problem by using Newtons second law for a rigid body. The only part I'm confused about is on what the moment of inertia should be. I think Its either (.5mr^2) or (.5mr^2 +mr^2)?
The moment of inertia depends on what you are using as the rotational axis; either expression will work, if you're careful.

ripper9100 said:
im also iffy on the net Torque. I am thinking that friction is the only force causing torque since the 45 N force is acting on the cylinders center.
Again, it depends on the axis of rotation. If you are using the center of mass as the axis, then you are correct.

Even though you have a choice, I recommend using the center of mass of the cylinder as your axis--I think it gives the best understanding of what's going on.
 
  • #7
what about the friction force is it up the incline or down the incline? I am confused about because usually the direction of friction force is opposite the direction of motion.
 
  • #8
Remember that friction acts to oppose slipping between surfaces. If there were no friction, which way would the surfaces (cylinder bottom and incline) slip with respect to each other? Use that to figure which way friction must act.
 

FAQ: Calculating Angular Acceleration with Friction on an Inclined Plane

What is rotation without slipping?

Rotation without slipping is a type of motion where an object rotates around a fixed axis without any slipping or sliding of its surface. This can occur when an object is rolling along a surface without any external forces causing it to slip or when an object is being rotated by a fixed point without any friction.

How is rotation without slipping different from sliding or slipping?

Rotation without slipping is different from sliding or slipping because it involves both rotational and translational motion. In rotation without slipping, the object's center of mass moves along a circular path while its surface maintains contact with the surface it is rolling on. In sliding or slipping, the object's surface slides or slips along the surface it is in contact with, without any rotational motion.

What factors affect rotation without slipping?

The main factors that affect rotation without slipping are the mass and shape of the object, the surface it is rolling on, and the presence of any external forces. Objects with larger masses and irregular shapes may have a harder time maintaining rotation without slipping, while smoother surfaces and absence of external forces can help maintain it.

What is the equation for rotational motion without slipping?

The equation for rotational motion without slipping is v = ωr, where v is the linear velocity of the object, ω is the angular velocity, and r is the distance from the object's center of mass to the point of rotation. This equation shows the relationship between the linear and angular velocities in rotation without slipping.

How is rotation without slipping used in real life?

Rotation without slipping is used in many real-life applications, such as in the wheels of vehicles, gears in machinery, and even in sports like bowling and skating. It is also utilized in engineering and physics to study the motion of objects and design systems that require smooth rotation without slipping.

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