Question

Two uniform solid spheres have the same mass, 1.65 kg, but one has a radius of 0.256 m while the other has a radius of 0.844 m. For each of the spheres, find the torque required to bring the sphere from rest to an angular velocity of 357 rad/s in 10.5 s. Each sphere rotates about an axis through its center.

a)Torque on sphere with the smaller radius.

b)Torque on sphere with the larger radius.

c)For each sphere, what force applied tangentially at the equator would provide the needed torque?Force on sphere with the smaller radius.

d)Force on sphere with the larger radius.

Answer 1

we remember that:

$\tau = I\alpha = \frac{2}{5}MR^2 \alpha$

a) With smaller radius

$\tau = \frac{2}{5}(1.65)(0.256)^2 \left ( \frac{357}{10.5} \right ) = 1.471 Nm$

b) With larger radius

$\tau = \frac{2}{5}(1.65)(0.844)^2 \left ( \frac{357}{10.5} \right ) = 15.98 Nm$

c) remember that:

$\tau = FR$

so:

c) For the samller radius:

$\tau =1.471/0.256 = 5.746 N$

d) For the larger raidus:

$\tau =15.98/0.844= 18.93 N$