Help I'm feeling stupid. :( ("A solid sphere rolls down an incline)

AI Thread Summary
A solid sphere rolls down an incline with a given linear acceleration of 1.21 m/s², prompting a discussion on how to find the angle of the incline. The equation a = g * sin(θ) is relevant, but the presence of friction complicates the situation, as it affects the sphere's rolling motion. Participants clarify that mass is not needed for the calculation since it cancels out in the equations. The confusion arises from the difference in how linear acceleration is presented in various problems, with some using 'g' as a reference. Understanding the role of rotational inertia and friction is crucial for accurately solving the problem.
Qwurticus
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Homework Statement



"A solid sphere rolls down an incline plane without slipping. If the center of mass of the sphere has a linear acceleration of 1.21 m/s2, what is the angle of the incline to the horizontal?"

Homework Equations



a = g * sin(θ)

The Attempt at a Solution



I got home from a long day at work and can't seem to make my mind click on how to solve this problem. What's throwing me off is that the linear acceleration is given in m/s2, but when I googled some similar problems to this one and they all give the linear acc. in 'g'. I think I need mass but I can't figure out how to get it or if I'm even correct.

Can someone help me? Am I over-complicating this, or am I just being incredibly stupid. :( Brain doesn't want to work.
 
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Qwurticus said:
What's throwing me off is that the linear acceleration is given in m/s2, but when I googled some similar problems to this one and they all give the linear acc. in 'g'.

"g" also has units of m/s^2 (g=9.8 m/s^2)

Qwurticus said:
I think I need mass but I can't figure out how to get it or if I'm even correct.

If you think you need mass, just use "m" in place of the mass and solve.

But let me ask you, does gravitational acceleration usually depend on mass?
 
Hi qwuarticus. Welcome to Physics Forums.

The equation you gave is correct if you can neglect the rotational inertia of the sphere. Otherwise, you need to take that into consideration. In either case, the mass of the sphere cancels out of the final result.

Chet
 
Qwurticus said:

Homework Equations


a = g * sin(θ)
This would be the acceleration if there was zero friction and the sphere was sliding down the incline, but there is a friction force involved that causes the sphere to roll. You need to fix this equation to take the friction force into account.
 
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