A few Rotational Kinetic Energy Questions?

[paul9619]

Hi there,

I am currently in the middle of studying for an exam in a few weeks time. I would appreciate it if someone could just have a quick look over the following details below and see if I am along the right lines.

1. A solid wheel of mass 15Kg is at the top of a slope 1in4. The slope is 1.5m high at the top. The radius of the wheel is 0.5m. There is no friction involved.

Firstly I have to find the speed of the wheel at the bottom of the slope!

I have used PE= mgh = 220.725J I then let this sum = the KE of 1/2mv^2 + 1/2Jw^2 (J being moment of Inertia) I then manipulated the forumla to find v at 4.43 m/s.

The next question asks that if the wheel did not roll on the way down would the speed be affected. I said yes and just took the KE Rotaional out of the question to find a different v.

Thirdly the question asked that if the slope was changed to 1in6 would the velocity be affected?? I answered no because the wheel would still be at the same height. Changing the slope would only chage the time it would take for the wheel to reach the bottom.

Am I along the right lines?

2. I have another question that asks how much power is required to drive a conveyor belt for the inital acceleration stage. The figures I have so far are as follows.

w= 6 rads/s, Pheta = 9 Rads. The initial angular acceleration is 2 rads/s. The wheel has a diameter of 0.4meters and a mass of 50kg. The belt has no mass.

Firstly I worked out KE rotational to give me 18 Joules.

Then am I right in saying that the torque is = J x angular rotation (J being Moment of Inertia). that gave me 2Newton Meters.

I then used Power = Torque x speed (I used (2Pi x w) for speed) that gave me 75.398 watts.

Am I along the right lines?

Any guidance much appreciated

 

[AlephZero]

1. You say "there is no friction involved" but then you say the wheel rolls. The only reason it will roll is because of friction between the wheel and the slope.

You assumed the friction was large enough to make it roll without any slipping.

Apart from that, your method for finding the speed when it rolls and when it slides are OK (but I didn't check your arithmetic). You are right, the angle of the slope doesn't affect the final speed.

2. Check the units. The initial angular acceleration can't be 2 rad/s because that is an angular velocity not accleration. It could be 2 rad/s^2.

Torque = J x angular acceleration (I'm not sure what you meant by "angular rotation"). Your answer of "2 Newton meters" seems wrong, the angular accel is 2 rad/s^2 (probably) but I don't think the wheel has J = 1.

Power = torque x angular velocity (again I'm not sure what you meant by "speed"). The angular velocities and accelerations in the question are given in rad/s and rad/s^2, so the factor of 2 pi shouldn't be in your equation.

 

[m2003]

Hi there,

It looks like you are on the right track with your calculations. For the first question, finding the speed of the wheel at the bottom of the slope, your approach using conservation of energy is correct. Just make sure to double check your calculations to ensure accuracy.

For the second question, you are correct in saying that the speed of the wheel would be affected if it did not roll down the slope. This is because without rolling, all of the potential energy would be converted into translational kinetic energy, resulting in a different final speed.

For the third question, you are also correct in saying that the velocity would not be affected by changing the slope. As you mentioned, the height of the wheel does not change, so the final speed would remain the same.

For the second set of questions, your approach to finding the power required to drive the conveyor belt is correct. Just make sure to double check your calculations and units to ensure accuracy. It may also be helpful to draw a free body diagram to visualize the forces acting on the wheel and belt.

I hope this helps and good luck on your exam!