Rotational Motion Question with Work Energy Theorem

In summary, when a 392-N wheel comes off a moving truck, rolls without slipping along a highway, and reaches the bottom of a hill with a rotational velocity of 25.0rad/s, the radius of the wheel is .6m and its moment of inertia about its rotation axis is 0.800MR2. Friction does work on the wheel as it rolls up the hill to a stop, with a work of 3500J in the opposite direction of motion. To calculate the height reached by the wheel, the work-energy theorem can be used with the given values of work done by friction, mass, radius, and moment of inertia. The unknowns, h and v, can be found by using the rotational
  • #1
Yosty22
185
4

Homework Statement



A 392-N wheel comes off a moving truck and rolls without slipping along a highway. At the bottom of a hill, it is rotating at 25.0rad/s. The radius of the wheel is .6m and its moment of inertia about its rotation axis is 0.800MR2. Friction does work on the wheel as it rolls up the hill to a stop, a height h above the bottom of the hill; this work has absolute value 3500J. Calculate h

Homework Equations



Work Energy Theorem

The Attempt at a Solution



I tried to use the work-energy theorem but I feel like I am missing the velocity of the center of mass of the wheel. I set up my equation as:

U1+K1+Wother=U2+K2 where "Wother is the work done by friction, in this case 3500J in the direction opposite of motion. Also, U1 cancels and I believe K2 should cancel out.

Therefore, my equation is:

3500J+.5mv2+.5Iω2=mgh

It seems like I have 2 unknowns, h and v. Am I missing something?
 
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  • #2
If you know omega, then you know v, because rolling without slipping means that every centimetre of distance moved by a point on the circumference of the wheel must correspond to the same number of centimetres of distance translated forward by the centre of mass of the wheel. Think about it and you'll see that if this weren't true, the wheel would have to be slipping.
 
  • #3
Hi Yosty22! :smile:
Yosty22 said:
At the bottom of a hill, it is rotating at 25.0rad/s. The radius of the wheel is .6m …

It seems like I have 2 unknowns, h and v. Am I missing something?

you can find v (the initial speed) from the 25.0 rad/sec :wink:
 

1. What is rotational motion?

Rotational motion refers to the movement of an object around an axis or center point. This type of motion is commonly seen in objects such as wheels, planets, and spinning tops.

2. How is rotational motion related to the Work Energy Theorem?

The Work Energy Theorem states that the work done on an object is equal to the change in its kinetic energy. In the case of rotational motion, this means that the torque applied to an object will result in a change in its angular velocity, thus affecting its kinetic energy.

3. What is torque?

Torque is a measure of the force that causes an object to rotate around an axis. It is calculated by multiplying the force applied to the object by the distance from the axis of rotation.

4. How is work done in rotational motion?

In rotational motion, work is done when a torque is applied to an object, causing it to rotate. This work is equal to the product of the torque applied and the angular displacement of the object.

5. Can the Work Energy Theorem be applied to all types of rotational motion?

Yes, the Work Energy Theorem can be applied to all types of rotational motion, as long as the conditions of the theorem are met. These conditions include a constant torque and a single axis of rotation.

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