State whether the following statements are true or false:
$(1)$ Torque produces angular velocity in an object.
$(2)$ For the rotational motion of a rigid body,the linear variables of all its particles are the same.

(N/A) $(1)$ False. Torque produces angular acceleration,not angular velocity.
$(2)$ False. In the rotational motion of a rigid body,all particles have the same angular variables (angular displacement,angular velocity,and angular acceleration),but their linear variables (linear displacement,linear velocity,and linear acceleration) differ depending on their distance from the axis of rotation.