Ch. 10: Rotational Motion and Angular Momentum

Question 1

An ultracentrifuge accelerates from rest to 9.87x10^5 rpm in 2.47 min. What is its angular acceleration in radians per second squared? (Formulas given)

Angular acceleration: _____ rad/s^2

What is the tangential acceleration of a point 9.70cm from the axis of rotation?

Tangential acceleration: ______ m/s^2

What is the radial acceleration in meters per second squared and in multiples of g of this point at full revolution per minute?

radial acceleration: _____ m/s^2

Radial acceleration in multiples of g: _____

Formulas:
Angular acceleration: a = Δ𝜔 / Δ𝑡

Tangential acceleration: at = angular acceleration * radius

radial acceleration: ar = w^2R

Answer 1

Angular acceleration: 697.4 rad/s^2

Tangential acceleration: 67.7 m/s^2

radial acceleration: 10.3 x 10^8 m/s^2

Radial acceleration in multiples of g: 10.5 x 10^7

Question 2

An engine flywheel initially rotates counterclockwise at 6.79 rev/s. Then over 23.7s, its rotation rate changes to 2.51rev/s in the clockwise direction. (Define counterclockwise rotation to be positive.)

Determine the flywheel’s average angular acceleration (a.avg)

a.avg = _____ rad/s^2

Answer 2

a.avg = -2.46 rad/s^2

Explanation:
a = Δ𝜔 / Δ𝑡
a = (w.f - w.i) / (t.f - t.i)
a =(-2.51 rev/s - 6.79 rev/s) / (23.7 s - 0s)
a = (-9.3 rev/s) / (23.7s)
a = -0.39 rev/s^2

Conversion:
-0.39 rev/s^2 * 2πrad / rev = -2.46 rad/s^2

Question 3

Define angular acceleration

Answer 3

the rate of change of angular velocity with time

Question 4

Define angular momentum

Answer 4

the product of moment of inertia and angular velocity

Question 5

Define change in angular velocity.

Answer 5

the difference between final and initial values of angular velocity

Question 6

Define kinematic of rotation motion

Answer 6

describes the relationships among rotation angle, angular velocity, angular acceleration, and time

Question 7

Define law of conservation of angular momentum

Answer 7

angular momentum is conserved, i.e., the initial angular momentum is equal to the final angular momentum when no external torque is applied to the system

Question 8

Define right-hand rule

Answer 8

direction of angular velocity ω and angular momentum L in which the thumb of your right hand points when you curl your fingers in the direction of the disk’s rotation

Question 9

Define moment of interia

Answer 9

mass times the square of perpendicular distance from the rotation axis; for a point mass, it isI=mr^2and, because any object can be built up from a collection of point masses, this relationship is the basis for all other moments of inertia

Question 10

Define rotational inertia

Answer 10

resistance to change of rotation. The more rotational inertia an object has, the harder it is to rotate

Question 11

Define rotational kinetic energy

Answer 11

the kinetic energy due to the rotation of an object. This is part of its total kinetic energy

Question 12

Define tangential acceleration

Answer 12

the acceleration in a direction tangent to the circle at the point of interest in circular motion

Question 13

Define torque

Answer 13

The turning effectiveness of a force

Question 14

Define work-energy theorem

Answer 14

if one or more external forces act upon a rigid object, causing its kinetic energy to change fromKE1KE1toKE2KE2, then the workWdone by the net force is equal to the change in kinetic energy

Question 15

How to calculate constant angular velocity?

Answer 15

ω=Δθ/Δt

w = angular veloctiy
Δθ = angle
t = time

Question 16

How to calculate angular acceleration?

Answer 16

α=Δω/Δt

a = acceleration
w = angular velocity
t = time

Question 17

How to calculate linear / tangential acceleration?

Answer 17

at=Δv/Δt

at = tangential acceleration (linear)
v = velocity
t = time

Question 18

For circular motion, note thatv=rω, so that….
at=Δ(rω)Δt.

Answer 18

at=Δ(rω)/Δt.

Question 19

Other important equations

Answer 19

The radius r is constant for circular motion, and soΔ(rω)=rΔω Thus, at=rΔωΔt.

By definition,Δω/Δt=α Thus, at=rα, or α=atr.