Rotational Motion Part 3Rotational Motion Part 3

By: Heather BrittonBy: Heather Britton

Rotational MotionRotational Motion

Rotational kinetic energy - the energy an object possesses by rotating

Like other forms of energy it is expressed in Joules (J)

Rotational kinetic energy - the energy an object possesses by rotating

Like other forms of energy it is expressed in Joules (J)

Rotational MotionRotational Motion

Recall that for translational motion KE = (1/2)mv2

v = ωr

Substituting for v we get

KE = (1/2)mω2r2

Recall that for translational motion KE = (1/2)mv2

v = ωr

Substituting for v we get

KE = (1/2)mω2r2

Rotational MotionRotational Motion

Rearranging we get

KE = (1/2)mr2ω2

I = mr2 so our equation for rotational KE becomes

KE = (1/2)Iω2

Rearranging we get

KE = (1/2)mr2ω2

I = mr2 so our equation for rotational KE becomes

KE = (1/2)Iω2

Rotational MotionRotational Motion

In regards to the law of conservation of energy, we now have a new quantity to consider

PEo + KEroto + KEtrano = PE + KErot + KEtran

In regards to the law of conservation of energy, we now have a new quantity to consider

PEo + KEroto + KEtrano = PE + KErot + KEtran

Example 8Example 8

A tennis ball, starting from rest, rolls down a hill (I = (2/3)mr2). It travels down a valley and back up the other side and becomes airborne at a 35o angle. The height difference between the starting point and launch point is 1.8 m. How far down range will the ball travel in the air?

A tennis ball, starting from rest, rolls down a hill (I = (2/3)mr2). It travels down a valley and back up the other side and becomes airborne at a 35o angle. The height difference between the starting point and launch point is 1.8 m. How far down range will the ball travel in the air?

Rotational MotionRotational Motion

Angular momentum - the rotational analog for linear momentum

Recall p = mv

Substituting for angular quantities we get the equation

Angular momentum - the rotational analog for linear momentum

Recall p = mv

Substituting for angular quantities we get the equation

Rotational MotionRotational Motion

L = Iω

ω = rotational velocity measured in rad/s

I = moment of inertia measured in kgm2

L = angular momentum measured in kgm2/s

L = Iω

ω = rotational velocity measured in rad/s

I = moment of inertia measured in kgm2

L = angular momentum measured in kgm2/s

Rotational MotionRotational Motion

Just like impulse F = p/Δt, there is an analog for rotation

See your book for the derivation of the following equation

τ = Iα

Just like impulse F = p/Δt, there is an analog for rotation

See your book for the derivation of the following equation

τ = Iα

Rotational MotionRotational Motion

The law of conservation of angular momentum - the total angular momentum of a rotating body remains constant if the net torque acting on it is zero

The law of conservation of angular momentum - the total angular momentum of a rotating body remains constant if the net torque acting on it is zero

Rotational MotionRotational Motion

Think of a figure skater.....

They spin very fast when they tuck their arms in they spin very fast

When they extend their arms, the rate of rotation slows

Angular momentum is conserved

Think of a figure skater.....

They spin very fast when they tuck their arms in they spin very fast

When they extend their arms, the rate of rotation slows

Angular momentum is conserved

Example 9Example 9

An artificial satellite is placed into an elliptical orbit about Earth. The point of closest approach (perigee) is rp = 8.37 x 106 m from the center of Earth. The greatest distance (apogee) is ra = 2.51 x 107 m. V at the perigee is 8450 m/s. What is the speed at the apogee?

An artificial satellite is placed into an elliptical orbit about Earth. The point of closest approach (perigee) is rp = 8.37 x 106 m from the center of Earth. The greatest distance (apogee) is ra = 2.51 x 107 m. V at the perigee is 8450 m/s. What is the speed at the apogee?