Question

g A has all the mass at the rim, while wheel B has the mass uniformly distributed, like a solid disk. The wheels have the same mass. The same torque is applied to both wheels. Which one accelerates faster in response to this torque?

Answer 1

Answer:

The second wheel

Explanation:

The torque is given by

$\tau=I\alpha$   (1)

where I is the moment of inertia and a is the angular acceleration. If we take into account the moment of inertia of a disk and a ring ()for the first wheel) we have:

$I_r=mR^2\\I_d=\frac{1}{2}mR^2$

where we used that both wheel have the same mass. By replacing in (1) we obtain:

$\alpha_r=\frac{\tau}{I_r}=\frac{\tau}{mR^2}\\\alpha_d=\frac{\tau}{I_d}=\frac{\tau}{\frac{1}{2}mR^2}=2\alpha_r$

Hence, the second wheel (the disk) has a greater acceleration.

hope this help!!

Answer 2

Answer:

The rim accelerates faster than the disk in response to the torque.

Explanation:

Given:

For the rim:

mass = M

radius = R

The moment of inertia is:

$I_{A} =MR^{2}$

For the disc:

mass = M

radius = 2R

The moment of inertia is:

$I_{B} =\frac{1}{2} M(2R)^{2} =2MR^{2}$

If the same torque is applied, thus:

$\tau _{A} =\tau _{B} \\I_{A}\alpha _{A} =I_{B}\alpha _{B} \\MR^{2}\alpha _{A}=2MR^{2}\alpha _{B} \\\alpha _{A}=2\alpha _{B}$

According to this result, the rim accelerates faster than the disk.