Solving Rotational Dynamics Problem: Finding Magnitude of Force

• zachattackback
In summary: I have to create a force that is greater than the force of gravity combined with the normal force. This force is called the lift force. So the equation to find the lift force would be F+N=G. So in summary, the wheel will leave the ground when the torque from the horizontal force is greater than the torque from gravity.
zachattackback
I have a quiz tommorrow and i am reviewing the harder problems and i can't get started on this one

A bicycle Wheel is resting against a small step whose height is h=0.120 m. The weight and radius of the whell are W=25.0N and r=0.340 m. A horizontal force F is applied to the axle of the whell. As the magnitude of F increases, there comes a time when the wheel just begins to rise up and loses contact with the ground. What is the magnitude of the force when this happenes?

I don't kinwo where to start i knwo the formulas
t=FL
and that the sum of the forces =0 but i don't know where to start

thanks

When the wheel starts to move, it will be rotating about the point of contact with the step. You will want to investigate torques and moment of inertia about that point.

do u ahve to make the force perpendicular to the point f contact so one equation would be Frcos45=t

then i don't knwo where to go i am trying to make stuff up to trigger my mind

zachattackback said:
do u ahve to make the force perpendicular to the point f contact so one equation would be Frcos45=t

then i don't knwo where to go i am trying to make stuff up to trigger my mind
What is the torque about the point of contact from the force acting at the point of contact? The only other forces are the applied horizontal force on the axle and gravity. The torques related to those forces will depend on the height of the step and the radius of the wheel. The torque for the horizontal force is easy to find in terms of F. The one for gravity is a bit tougher, but you can get it from the geometry of the problem.

can u maybe help me with an equation i am confused on what u are saying

zachattackback said:
can u maybe help me with an equation i am confused on what u are saying

Draw a circle to represent the wheel and a horizontal tangent below the wheel to represent the ground. Draw the step of height h with the corner touching the wheel. Mg acts downward at the center of the wheel. F acts horizontally toward the step. The distance between the line of F and the contact point is r-h. The torque is F(r-h). Draw a radius from the center of the wheel straight down and another from the center to the point of contact. Call the angle between these radii θ. r-h can be written in terms of r and θ, so θ can be determined from r and h. The distance between the line of mg and the contact point can be written in terms of r and θ, and the torque from gravity is this distanve times mg. When F is big enough to make the F torque greater than the mg torque, the wheel will leave the ground.

Say I am standing on the ground. As we know, gravity is acting on me. But why am I not sinking into the ground? Because there is an opposite force acting on me, this force is called the Normal force. If I want to lift off the ground, what do I have to do?

1. What is rotational dynamics and why is it important?

Rotational dynamics is the study of the motion of objects that rotate around a fixed axis. It is important because it helps us understand the behavior of objects such as wheels, gears, and propellers, and allows us to predict their motion and forces acting upon them.

2. How do you calculate the magnitude of force in a rotational dynamics problem?

To calculate the magnitude of force in a rotational dynamics problem, you can use the equation F = ma, where F is the force, m is the mass of the object, and a is the acceleration of the object. In rotational dynamics, the acceleration is given by a = rα, where r is the distance from the axis of rotation to the object and α is the angular acceleration.

3. What is the difference between torque and force in rotational dynamics?

Force and torque are both important concepts in rotational dynamics. Force is a push or pull that causes an object to accelerate, while torque is a force that causes an object to rotate. In other words, force is a linear concept, while torque is a rotational concept. Additionally, torque takes into account the distance from the axis of rotation, while force does not.

4. How do you determine the direction of the force in a rotational dynamics problem?

The direction of the force in a rotational dynamics problem can be determined by using the right-hand rule. This rule states that if you point your right thumb in the direction of the angular velocity, your fingers will curl in the direction of the torque. This can then be used to determine the direction of the force acting on the object.

5. Can you provide an example of a real-life application of rotational dynamics?

One example of a real-life application of rotational dynamics is the design of bicycle gears. By understanding rotational dynamics, engineers can design gear systems that allow for efficient transfer of power from the rider's legs to the wheels, resulting in a smoother and more efficient ride.

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