ANGULAR IMPULSE

Crucifixion (Corpus Hypercubus)

Salvador Dali, 1954

LINEAR AND ANGULAR MOMENTUM

Recall that linear momentum was defined as mass x velocity

p = mv

Angular momentum is defined as moment of inertia x angular velocity

L = Iω

Angular momentum is a vector, the direction of the vector is defined by the right hand rule. (Link to awesome!) You do not need to know about direction for this course.

The units for angular momentum are kg m²/s

Angular momentum describes the quantity of rotation that a body possesses.

COMPUTING ANGULAR MOMENTUM

The diver shown to the right is rotating with an angular velocity of 4.2 rad/s and has a moment of inertia of 5 kg m². Compute the magnitude of the diver’s angular momentum.

ANGULAR IMPULSE-ANGULAR MOMENTUM RELATIONSHIP

EXAMPLE

• A variable torque is applied for 0.90 s to a 2.13 kg bar that has a length of 0.75 m and is initially at rest. A graph of the torque is shown to the right.

EXAMPLE

• A variable torque is applied for 0.90 s to a 2.13 kg bar that has a length of 0.75 m and is initially at rest. A graph of the torque is shown to the right.
• The average of the torque over the 0.90 s is 3.72 Nm.
• Determine the final angular velocity of the bar.

​

EXAMPLE

• How could you graphically determine the impulse applied to the bar?

​

EXAMPLE

A constant torque of 4.55 Nm is applied to a rigid bar with a moment of inertia of 0.80 kg·m² that is initially at rest.

1. What angular impulse is applied to the bar?
2. What is the final angular velocity of the bar?

THINK ABOUT: �TORQUE, ANGULAR VELOCITY, AND ANGULAR MOMENTUM

Dry Erase Board Analysis Time!

Create qualitative graphs for each of the following i) before leaving the ground and ii) after leaving the ground. Be able to justify your graphs using appropriate physics concepts.

1. Torque vs. time
2. Angular velocity vs. time
3. Angular momentum vs. time

a) Torque vs. Time

Before Leaving Ground

After Leaving Ground

b) Angular Velocity vs. Time

Before Leaving Ground

After Leaving Ground

c) Angular Momentum vs. Time

Before Leaving Ground

After Leaving Ground

Example

Simone Biles

• 4’8” (1.42 m)
• 104 lb (47.2 kg)

Shaquille O’Neal

• 7’1” (2.16 m)
• 324 lb (147 kg)

​

Each person will perform a double layout (no twist) in 1.12 s. Calculate the following for each person to complete the two rotations.

• Angular velocity
• Angular momentum
• The force required to create the rotational motion (assume push-off time is 0.15 s)

Example

Simone Biles

• 4’8” (1.42 m)
• 104 lb (47.2 kg)

Shaquille O’Neal

• 7’1” (2.16 m)
• 324 lb (147 kg)

​

• ω = Δθ / t

= 4π / 1.12 s

= 11.2 rad /s (for both)

Example

Simone Biles

• 4’8” (1.42 m)
• 104 lb (47.2 kg)

Shaquille O’Neal

• 7’1” (2.16 m)
• 324 lb (147 kg)

​

Example

Simone Biles

• 4’8” (1.42 m)
• 104 lb (47.2 kg)

Shaquille O’Neal

• 7’1” (2.16 m)
• 324 lb (147 kg)

​