A solid wood top spins at high speed on the floor, with a spin direction shown in figure 11.112

a. Using appropriately labeled diagrams, explain the direction of motion of the top (you do not need to explain the magnitude).

b. How would the motion change if the top had a higher spin rate? Explain briefly.

c. If the top were made of solid steel instead of wood, explain how this would affect the motion (for the same spin rate).

The angular momentum is defined as the multiplication of mass and the velocity of the object.

The top would move clockwise. The angular momentum vector of a top or gyroscope moves in the direction of the torque applied to it. The floor exerts a vertical normal force which acts towards the center of mass to the right. The cross product point out of the page that is clockwise. Meanwhile, the angular momentum of the top points upwards and to the right. The angular momentum vector is pushed towards the page, which is clockwise.

The precession would slow down. From section 11.11 a higher spin rate means a lower precession rate. The spin of the top creates rotational angular momentum which is rotated by the normal force. The larger the rotational angular momentum, the more difficult it is to move. Since the strength of the torque which moves the rotational angular momentum is not dependent on the spin, and the magnitude of the rotational angular momentum is proportional is proportional to the top’s spin, a greater spin results in a larger rotational angular momentum that is more difficult to move.

A solid steel top would be heavier. From section 11.11 the rate of precession is proportional to the mass of the object. This is because greater mass means a stronger normal force, which means a stronger torque. A stronger torque moves the angular momentum vector quicker vector quicker than a weaker torque.