A nanomechanical (NEMS) gyroscope includes an integrated circuit substrate, a pair of spaced apart contact pads disposed on the substrate, and a movable nanoscale element forming at least a portion of a first electrically conductive path electrically coupling the contact pads. The movable element experiences movement comprising rotation, changes in rotation, or oscillation upon the gyroscope experiencing angular velocity or angular acceleration. Movement of the gyro introduces geometrically induced phase changes which results in phase and/or frequency changes in ac current flowing through the movable element. An inertial measurement unit (IMU) can include an integrated circuit substrate having a three axis gyroscope formed on the substrate and a three axis accelerometer, which is preferably formed on the same substrate.