Name: lawn roller angular acceleration with friction
Uploaded: 2024-03-07T13:22:25.000Z
Duration: 1 min 16 s
Channel: JoVE

Consider a lawn roller of mass 100 kg, a radius of 0.2 meters, and a radius of gyration of 0.15 meters. If a force of 200 N is applied with an angle of 60 degrees with the horizontal, then what is the angular acceleration of the lawn roller?
The coefficient of static friction between the ground and the lawn roller is 0.15, and the coefficient of kinetic friction is 0.1.
Assuming rolling without slipping, the moment of the point of zero instantaneous velocity, point A, is calculated using a horizontal component of the applied force.
At point A, the moment of inertia is calculated using the parallel axis theorem.
Substituting the value of the moment of inertia at point A in the moment equation gives the value of angular acceleration.
The assumption of rolling without slipping motion is valid if the frictional force resulting from the movement of the lawn roller&#39;s center is lower than the maximum static frictional force.

equation of motion: general plane motion - problem solving

Equation of Motion: General Plane motion - Problem Solving

Consider a lawn roller with a mass of 100 kg, a radius of 0.2 meters, and a radius of gyration of 0.15 meters. A force of 200 N is applied to this roller, angled at 60 degrees from the horizontal plane. What will be the angular acceleration of the lawn roller?
The friction between the roller and the ground is characterized by two coefficients. The static friction coefficient is 0.15, while the kinetic friction coefficient is 0.1. These values are crucial in understanding the interaction between the roller and the surface on which it moves. The concept of rolling without slipping is assumed in this scenario. In this context, the moment of the point of zero instantaneous velocity is calculated. This calculation is made using the horizontal component of the applied force.
<img alt="Static equilibrium equation \( M_A = F \cos(60^\circ)R \); torque calculation formula." src="/files/ftp_upload/15544/15544_Equation_PT_001.svg" style="text-align: center; height: 14px;" data-altupdatedat="1762173717000" data-alt="Equation 1" />
The point of zero instantaneous velocity also serves as a reference for the calculation of the moment of inertia, derived using the parallel axis theorem.
<img alt="Moment of inertia formula \( I_A = I_G + mR^2 \) equation in physics diagram." src="/files/ftp_upload/15544/15544_Equation_PT_002.svg" style="text-align: center; height: 20px;" data-altupdatedat="1762173717000" data-alt="Equation 2" />
Once the moment of inertia is determined, it is substituted into the moment equation, subsequently providing the sought-after value of angular acceleration.
<img alt="Torque equation MA=IA&#945; for rotational motion analysis, illustrating dynamics concept." src="/files/ftp_upload/15544/15544_Equation_PT_003.svg" style="text-align: center; height: 14px;" data-altupdatedat="1762173717000" data-alt="Equation 2" />
However, it is important to note that the assumption of rolling without slipping is only valid under certain conditions. Specifically, the frictional force resulting from the movement of the lawn roller's center must be lower than the maximum static frictional force. Only then can the roller move without slipping.

Consider a lawn roller of mass 100 kg, a radius of 0.2 meters, and a radius of gyration of 0.15 meters. If a force of 200 N is applied with an angle of 60 ...

equation-of-motion-general-plane-motion-problem-solving

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Planar Kinematics of a Rigid Body

KEY TERMS AND CONCEPTS

lawn roller angular acceleration with friction

A lawn roller’s angular acceleration can be found by using rolling motion and friction. The roller in this problem has a mass of 100 kg, a radius of 0.2 meters, and a radius of gyration of 0.15 meters. A force of 200 N is applied at an angle of 60 degrees from the horizontal.

The setup also includes friction between the roller and the ground. The static friction coefficient is 0.15, and the kinetic friction coefficient is 0.1. The motion is treated as rolling without slipping, so the point of zero instantaneous velocity is used as the reference point. The horizontal component of the applied force is used to find the moment about that point.

The moment of inertia is then found with the parallel axis theorem. After that, it is placed into the moment equation to determine the angular acceleration of the lawn roller. The no-slip assumption is valid only if the friction force from the roller’s center motion stays below the maximum static friction force. If that condition is not met, the roller would not roll without slipping.

Lawn Roller Angular Acceleration with Friction

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A lawn roller’s angular acceleration can be found by using rolling motion and friction. The roller in this problem has a mass of 100 kg, a radius of 0.2 meters, and a radius of gyration of 0.15 meters. A force of 200 N is applied at an angle of 60 degrees from the horizontal. The setup also includes friction between the roller and the ground. The static friction coefficient is 0.15, and the kinetic friction coefficient is 0.1. The motion is treated as rolling without slipping, so the point of...

key terms and concepts

Find the angular acceleration of a lawn roller using rolling without slipping, friction coefficients, the parallel axis theorem, and the moment equation.

Lawn Roller Angular Acceleration with Friction | JoVE K12

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Lawn Roller Angular Acceleration with Friction

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