# Angular Momentum and Torque

In the figure (please see the attachment), a 0.420 kg ball is shot directly upward at initial speed 37.5 m/s. What is its angular momentum about P, 2.20 m horizontally from the launch point, when the ball is at the following heights?

i) at max height, ii) when it is halfway to the ground.

Also find the torque on the ball about P at max height and halfway to ground.

Â© BrainMass Inc. brainmass.com October 2, 2022, 5:16 am ad1c9bdddfhttps://brainmass.com/physics/angular-momentum/angular-momentum-torque-256844

## SOLUTION This solution is **FREE** courtesy of BrainMass!

Angular momentum of a particle about a point is defined as the moment of the linear momentum vector about the given point i.e. :

Magnitude of angular momentum = Magnitude of the linear momentum vector x Perpendicular distance of the line of action of the linear momentum vector from the given point

Perpendicular distance of the linear momentum vector from the given point = 2.2 m

a) Velocity of the ball at the highest point = 0

Linear momentum at the highest point = 0

Angular momentum at the highest point = 0

b) Initial kinetic energy of the ball = Â½ mv2

At the highest point the ball will have only potential energy, Hence, mgh = Â½ mv2

Or h = v2/2g = 37.52/2x9.8 = 71.75 m

_______

After falling through Â½ the height (i.e. 35.9 m), its velocity will be v' = âˆš2g(35.9) =

__________ ______

âˆš2x9.8x(35.9) = âˆš703.64 = 26.5 m/s

Linear momentum of the ball at Â½ the height = mv = 0.42 x 26.5 = 11.13 kg.m/s

Magnitude of angular momentum = 11.13 x 2.2 = 24.5 kg.m2/s.

As the ball moves clockwise with respect to the given point, the direction of the angular momentum vector is into the x-y plane i.e. towards -z axis.

c) At any point between the lowest and the highest point, the ball is subjected to a force equal to its weight i.e. 0.42 x 9.8 = 4.1 N

Torque is defined as the moment of the force vector about the given point i.e. :

Torque = Magnitude of the force vector x Perpendicular distance of the line of action of the force vector from the given point

Hence, torque at all points between the lowest and the highest points = 4.1 x 2.2 = 9 Nm (towards -z axis).

Â© BrainMass Inc. brainmass.com October 2, 2022, 5:16 am ad1c9bdddf>https://brainmass.com/physics/angular-momentum/angular-momentum-torque-256844