Calculate Work Needed to Stop Rolling Cylinder

In summary, to stop the homogeneous cylinder of radius 30cm and mass 40kg rolling without slipping at 2.4m/s, we need to consider both the linear kinetic energy and the rotational kinetic energy. The total kinetic energy is the sum of these two energies, which can be calculated using the formulas KE_linear = 0.5 * mass * velocity^2 and KE_rotation = 0.5 * moment of inertia * angular velocity^2. By plugging in the given values, we can find the total kinetic energy to be approximately 115 Joules.
  • #1
ViewtifulBeau
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A homogeneous cylinder of radius 30cm and mass 40kg is rolling without slipping along a horizontal floor at 2.4m/s. How much work is needed to stop the cylinder?

work = delta_KE in this case so oi figured .5 *40 * 2.4^2 = 115 J but this is not right, what should i do with the cylinder?
 
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  • #2
i still can not figure this one out.
 
  • #3
Besides KE of the center-of-mass moving in translation (linear),
you also have KE of the extended mass moving AROUND the c.o.m.

KE_rotation = 1/2 I (omega)^2
 
  • #4
i did this and found omega to be 8 rad/s and I to be 1.8 then i found the KE to be 57.6 this is now right either.
 
  • #5
"Besides" the old linear KE there's now rotational KE, ALSO.
The total KE is the SUM : KE_linear + KE_rotation
 

What is the formula for calculating the work needed to stop a rolling cylinder?

The formula for calculating the work needed to stop a rolling cylinder is W = 1/2 * I * ω2, where W is the work, I is the moment of inertia, and ω is the angular velocity.

What is the moment of inertia of a rolling cylinder?

The moment of inertia of a rolling cylinder depends on its mass, radius, and shape. For a solid cylinder, the formula for moment of inertia is I = 1/2 * m * r2, where m is the mass and r is the radius.

How does the surface on which the cylinder is rolling affect the work needed to stop it?

The surface on which the cylinder is rolling can affect the work needed to stop it due to friction. If the surface is rough, there will be more friction and therefore more work needed to stop the cylinder. If the surface is smooth, there will be less friction and less work needed to stop the cylinder.

Does the direction of the cylinder's rotation affect the work needed to stop it?

Yes, the direction of the cylinder's rotation does affect the work needed to stop it. If the cylinder is rotating in the same direction as the force applied to stop it, less work will be needed. If the cylinder is rotating in the opposite direction, more work will be needed.

What are some real-world applications of calculating work needed to stop a rolling cylinder?

Calculating the work needed to stop a rolling cylinder can be useful in various industries, such as engineering and physics. For example, it can be used to analyze the energy required to stop a rotating machine part or to design braking systems for vehicles. It can also be used in sports, such as calculating the work needed to stop a rolling ball in a game of bowling or billiards.

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