Angular Momentum

Angular Momentum

• MOMENTUM RESULTING FROM AN OBJECT MOVING IN LINEAR MOTION IS CALLED LINEAR MOMENTUM.

• MOMENTUM RESULTING FROM THE ROTATION (OR SPIN) OF AN OBJECT IS CALLED ANGULAR MOMENTUM.

Conservation of Angular Momentum

• ANGULAR MOMENTUM IS IMPORTANT BECAUSE IT OBEYS A CONSERVATION LAW, AS DOES LINEAR MOMENTUM.

• THE TOTAL ANGULAR MOMENTUM OF A CLOSED SYSTEM STAYS THE SAME.

Calculating angular momentumANGULAR MOMENTUM IS CALCULATED IN A SIMILAR WAY TO

LINEAR MOMENTUM, EXCEPT THE MASS AND VELOCITY ARE REPLACED BY THE MOMENT OF INERTIA AND ANGULAR VELOCITY.

Angularvelocity

(rad/sec)

ANGULARMOMENTUM(KG M/SEC2)

L = I w Moment of inertia(kg m2)

1. You are asked for angular momentum.2. You are given mass, shape, and angular velocity. – Hint: both rotate about y axis.

3. Use L= Iw, Ihoop = mr2, Ibar = 1/12 ml2

Calculating angular momentumAn artist is making a moving metal sculpture. She takes two identical 1 kg metal bars and bends one into a hoop with a radius of 0.16 m. The hoop spins like a wheel. The other bar is left straight with a length of 1 meter. The straight bar spins around its center. Both have an angular velocity of 1 rad/sec. Calculate the angular momentum of each and decide which would be harder to stop.

TORQUE

WHEN QUARTERBACKS THROW THE FOOTBALL, THEY IMPART A SPIN WITH THEIR FINGERS, SO THAT THE BALL SPINS RAPIDLY AS IT FLIES THROUGH THE AIR. FOOTBALL FANS CALL A GOOD PASS A TIGHT SPIRAL.

BULLETS WHICH COME OUT OF A RIFLED BARREL HAVE GROOVES CUT INTO THEM, LIKE THIS ONE. THESE LEAVE BALLISTIC FINGER PRINTS

ANGULAR MOMENTUM

3. Solve hoop: Ihoop= (1 kg) (0.16 m)2 = 0.026 kg m2

– Lhoop= (1 rad/s) (0.026 kg m2) = 0.026 kg m2/s

4. Solve bar: Ibar = (1/12)(1 kg) (1 m)2 = 0.083 kg m2

– Lbar = (1 rad/s) (0.083 kg m2) = 0.083 kg m2/s

5. The bar has more than 3x the angular momentum of the hoop, so it is harder to stop.

Calculating angular momentum

12.3 Gyroscopes angular momentum

• A gyroscope is a device that contains a spinning object with a lot of angular momentum.

• Gyroscopes can do amazing tricks because they conserve angular momentum.

• For example, a spinning gyroscope can easily balance on a pencil point.

12.3 Gyroscopes angular momentum

• A gyroscope on the space shuttle is mounted at the center of mass, allowing a computer to measure rotation of the spacecraft in three dimensions.

• An on-board computer is able to accurately measure the rotation of the shuttle and maintain its orientation in space.