PHYS $1111$K: Introductory Physics I

$(10$ Points$)$ Consider a person who spins a large grindstone by placing her hand on its edge and exerting a force through part of a revolution. The force is kept perpendicular to the grindstone's $0\mathrm{.}320-m$ radius at the point of application, and the effects of friction are negligible.

a$.(3$ Points$)$ How much work is done if she exerts a force of $200$ N through a rotation of $1$ rad?

b$.(3$ Points$)$ What is the final angular velocity, if the grindstone has a mass of $85\mathrm{.}0$ kg $?$

c$.(2$ Points$)$ What is the final rotational kinetic energy?

d$.(2$ Points$)$ What is the angular acceleration of the grindstone?

e$.(5$ Bonus$)$ How long did the grindstone take to reach the $1$ rad rotational angle from the start of motion?