An astronaut rotates at the end of the test machine whose arm has a length of $10.0\mathrm{m}$, as shown in the diagram. The acceleration she experiences must not exceed $5g \left(\mathrm{Take}, g=10\mathrm{m}/{\mathrm{s}}^2\right)$.

Determine the maximum number of revolutions per minute of the arm.

A body of mass $1.00 \mathrm{kg}$ is tied to a string and rotates on a horizontal, frictionless table.

a. The length of the string is $40.0\mathrm{cm}$ and the speed of revolution is $2.0 \mathrm{m}/\mathrm{s}$. Calculate the tension in the string.

A body of mass $1.00 \mathrm{kg}$ is tied to a string and rotates on a horizontal, frictionless table. The length of the string is $40.0\mathrm{cm}$.

b. The string breaks when the tension exceeds $20.0\mathrm{N}$. Determine the largest speed the mass can rotate at?

A body of mass $1.00 \mathrm{kg}$ is tied to a string and rotates on a horizontal, frictionless table. 

c. The breaking tension of the string is $20.0\mathrm{N}$ but you want the mass to rotate at $4.00 \mathrm{m}/\mathrm{s}$. Determine the shortest length string that can be used.

A neutron star has a radius of $50.0\mathrm{km}$ and completes one revolution every $25\mathrm{ms}$.

a. Calculate the centripetal acceleration experienced at the equator of the star.

A neutron star has a radius of $50.0\mathrm{km}$ and complete one revolution every $25\mathrm{ms}$.

b. The acceleration of free fall at the surface of the star is $8.0\times {10}^{10} \mathrm{m}/{\mathrm{s}}^2$. State and explain whether a probe that landed on the star could stay on the surface or whether it would be thrown off.

The earth $\left(\mathrm{mass}=6.0\times {10}^{24}\mathrm{kg}\right)$ rotates around the Sun in an orbit that is approximately circular, with a radius of $1.5\times {10}^{11} \mathrm{m}$.

a. Estimate the orbital speed of the earth around the sun.

The earth $\left(\mathrm{mass}=6.0\times {10}^{24}\mathrm{kg}\right)$ rotates around the Sun in an orbit that is approximately circular, with a radius of $1.5\times {10}^{11} \mathrm{m}$.

b. Determine the centripetal acceleration experienced by the earth.