Calculating Rolling Motion: Solving for Time on an Incline without Given Mass

[hoseA]

A spherical object has a(n) 54.4 m diameter.
Its moment of inertia about a diameter is
I = fMR^2, where M is its mass, R is its
radius, and f = 0.302.
The acceleration of gravity is 9.8 m/s^2
Starting from rest, how long will it take this
object to roll, without slipping, 10.88 m down
an incline that makes an angle of 35.1 degrees with
the horizontal? Answer in units of s.

How does I figure this out without a given mass? Does it cancel out in the calculation?

An approach to this and concepts involved in solving this would help greatly.

I don't know, I don't like moment of interia nor torque. :(

I have my final exam tomorrow, help is greatly needed and much appreciated.

 

[Doc Al]

Start by identifying the forces that act on the object. Then apply Newton's 2nd law for both translation and rotation to find the acceleration of the object down the incline. (Since it rolls without slipping, figure out how the translational motion is related to the rotational motion.)

 

[hoseA]

Mgh= 1/2mv^2 + 1/2 Iw^2

I can use v=Rw to substitute into the equation and eventually solve for v.

But then how do I find alpha to solve for t?

w= alpha * t

 

[Aneleh]

Newtons second law... F=ma; torque=I(alpha)

 

[hoseA]

alpha = (gsin(theta))/(R + (I/mr))

t came out to be equal to 2.24226 s. (which is correct )

Thanks to all those that helped!

 

[Gamma]

Just a correction:

w= alpha * t

dw = alpha * dt

Good luck on your exam.

 

[hoseA]

Good luck on your exam.

Thanks... I really need an A. :)

 

[Doc Al]

Mgh= 1/2mv^2 + 1/2 Iw^2

I can use v=Rw to substitute into the equation and eventually solve for v.

There's nothing wrong with solving the problem this way. Once you solve for the final velocity at the bottom of the incline, you can use simple kinematics to find the time. Hint: What's the average speed of the object as it rolls down the incline?