How Is Linear Velocity Calculated for a Cylinder on an Inclined Plane?

[kayron]

Homework Statement

A cylinder of radius 20cm and mass 100g rolls down an inclined plane of height 60cm without slipping. the linear velocity of the cylinder at the bottom is?? (g=980cm/s/s)

 

[gneill]

What concepts do you think might be applicable? What formulas correspond to them?
You'll have make some attempt to work the problem before we can help you with it!

 

[kayron]

is that really necessary?? why?

 

[Quinzio]

It's the forum philosophy.

 

[rwisz]

The linear velocity of the cylinder at the bottom of the inclined plane can be calculated using the equation v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the radius of the cylinder.

First, we need to calculate the angular velocity of the cylinder. Since the cylinder is rolling without slipping, we can use the equation ω = v/r, where v is the linear velocity and r is the radius.

Using the equation v = √(2gh), where g is the acceleration due to gravity and h is the height of the inclined plane, we can calculate the linear velocity of the cylinder at the bottom of the inclined plane.

v = √(2*980cm/s/s*60cm) = 392cm/s

Now, we can plug this value into the equation ω = v/r to find the angular velocity.

ω = 392cm/s / 20cm = 19.6 rad/s

Finally, we can use the equation v = ωr to calculate the linear velocity at the bottom of the inclined plane.

v = 19.6 rad/s * 20cm = 392cm/s

Therefore, the linear velocity of the cylinder at the bottom of the inclined plane is 392cm/s.