Question 1
1 answer:
Newton's second law for rotational motion allows us to find that the correct answer is:
D. The ball accelerated as it traveled down the ramp.
Newton's second law can be used for rotational motion, in this case we must take into account the torque that is the product of the force times the distance perpendicular to the point of rotation. For this situation the torque is proportional to the moment of inertia times the angular acceleration
τ = I α
The bold letters indicate vectors, τ el is torque, I the moment of inertia and α is the angular acceleration
In the case of the ball, we can approximate it to a sphere that has a tabulated moment of inertia with respect to its center of mass
I = m r²
Where m is the mass of the sphere and r its radius
In the attachment we can see a diagram of the forces in the system, the turning point is located at the point of contact of the sphere with the ramp, we can see that the arm (perpendicular distance) between several forces and this point is zero, the only force with a distance is the component x of the weight.
Wₓ r = I α
Angular and linear variables are related
a = r α
α =
We use trigonometry to find the components of the weight
cos θ =
sin θ =
Wₓ = W sin θ
τ = mg r sin θ
Let's substitute
mg r sin θ = m r²
a= g sin θ
We see that the center of mass has an acceleration.
Let's analyze the different claims:
A) False. It has an acceleration so its speed must change
B) False. The sphere is accelerated, so its position increases with time
C) False. Stable kinematics that velocity is the derivative of position
D) True. It agrees with the acceleration found.
In conclusion using Newton's second law for rotational motion we find that the correct answer is;
D. The ball accelerated as it traveled down the ramp.
Learn more about torque here:
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