Question

1. Read Section 11-3: we will consider the motion of a yo-yo moving downward on its string.

(a) In terms of the yo-yo’s mass m, its moment of inertia about the center-of-mass I, and the length of the string l, what is the angular speed ? of a “sleeping” yo-yo that started from rest and just finished rolling all the way down its string? You may assume that kinetic friction between the yo-yo and the string has not yet significantly slowed the yo-yo.

(b) A yo-yo consists of two flat disks of uniform density surrounding a low-mass axle. Each disk has mass m/2, the axle has radius r, and the yo-yo has radius R. What is the angular speed of the yoyo when it is halfway down the string? (Hint: consider Equation 11.2 from your textbook, but think carefully about what radius you should use.)

(c) In 1980, a large yo-yo was released from a crane over San Francisco Bay. The 116-kg yo-yo consisted of two uniform disks of radius 32 cm connected connected by an axle of radius 3.2 cm. What was the magnitude of the yo-yo’s acceleration during (1) its fall? What was the tension in the yo-yo’s cord? Be careful of your signs.

Answer #1

(A) KE_yoyo = m v^2 / 2 + I w^2 /2

and v = w r

KE = m w^2 r^2 / 2 + I w^2 / 2

Applying energy conservation,

PEi + Kei = PEf + KEf

m g L + 0 = 0 + (m r^2 + I) w^2 / 2

w = sqrt(2 m g L / (m r^2 + I )) .....Ans

(B) v = w r and I = 2(m/2)(R^2 /2) = m R^2 / 2

m g (L/2) = m (w r)^2 /2 + (m R^2 / ) w^2 / 2

g L = w^2 r^2 + R^2 w^2

w = sqrt(g L / (r^2 + R^2))

(c) m g - T = m a

and torque = I alpha

(0.032)T = (116 x 0.32^2 / 2)(a/0.032)

T = 11600 a

putting in 1st equation,

116 x 9.8 = (116 + 11600) a

a = 0.097 m/s^2

Tension = 11600a = 1125 N

A yo-yo has a rotational inertia of 1250 g·cm2 and a mass of 137
g. Its axle radius is 1.61 mm, and its string is 91.2 cm long. The
yo-yo rolls from rest down to the end of the string.
(a) What is the magnitude of its linear acceleration?
(b) How long does it take to reach the end of the string? As it
reaches the end of the string, what are its
(c) linear speed,
(d) translational kinetic energy,...

A yo-yo has a rotational inertia of 1100 g·cm2 and a
mass of 118 g. Its axle radius is 1.99 mm, and its string is 133 cm
long. The yo-yo rolls from rest down to the end of the string.
(a) What is the magnitude of its linear
acceleration? (b) How long does it take to reach
the end of the string? As it reaches the end of the string, what
are its (c) linear speed, (d)
translational kinetic energy,...

A yo-yo has a rotational inertia of 960 g·cm2 and a mass of 130
g. Its axle radius is 3.4 mm and its string is 100 cm long. The
yo-yo is thrown so that its initial speed down the string is 1.1
m/s. As the yo-yo reaches the end of the string, what are the
following values?
(a) its total kinetic energy
(b) its linear speed
(c) its translational kinetic energy
(d) its angular speed
(e) its rotational kinetic energy...

1. A yo-yo consists of two solid disks, each of mass M and
radius 3R. The two disks are connected by a rod of radius R and
negligible mass.
a.) The moment of inertia of the yo-yo about its axis of
symmetry is of the form ???^2 where ? is a number. What is ??
b.) Draw the extended free body diagram for the yo-yo and use it
to write Newton's 2nd law in terms of the magnitude of the...

Part A) yoyo is consists of two disks each for radius
.1m and mass .25kg attached by a
massless .02m diameter axle. A .8m long string is wrapped around
axle. The yoyo is
released from rest and allowed to unwind down the string spinning
faster and faster.
What is the linear velocity of the yoyo when the string has
unrolled its entire length?
Part B) When the yoyo reaches the end of the rope, it
begins to travel upward again...

A yoyo is consists of two disks each for radius .1m and mass
.25kg attached by a massless .02m diameter axle. A .8m long string
is wrapped around axle. The yoyo is released from rest and allowed
to unwind down the string spinning faster and faster. What is the
linear velocity of the yoyo when the string has unrolled its entire
length?
b. When the yoyo reaches the end of the rope, it begins to
travel upward again like a...

Please show work, I'm having trouble answering these :(
1)A bicycle with 0.3 m radius wheels, is moving such that the
angular speed of each wheel is 75 rad/s. If the bicyclist then
applies the brakes and the wheels slow with an angular acceleration
of -15 rad/s2, how many revolutions will each wheel make before the
bike stops?
A. 188 revolutions
B. 1.07e4 revolutions
1C.14.7 revolutions
D. 62.7 revolutions
E.29.8 revolutions
2)You tie the loose end of a 0.1 kg...

Consider an aluminum annular disk with an outer radius 63.2 mm
and inner radius 7.9 mm. The mass of the disk is 464 grams.
The disk is allowed to rotate on a frictionless table with the
rotation axis at its center. The disk has a small pulley rigidly
mounted at the top concentrically. The pulley's radius is 12.1 mm,
and the mass of the pulley is negligible. A string is wrapped
around the pulley, and a hanging mass of 19.3...

A solid uniform disk of mass M = 9.6 kg and radius R = 21 cm
rests with its flat surface on a frictionless table (i.e., the axis
of the cylinder is perpendicular to the table.) The diagram shows a
top view. A string is wrapped around the rim of the disk and a
constant force of F = 10.8 N is applied to the string. The string
does not slip on the rim.
1)
What is the acceleration of...

1. During the game against the Philadelphia Eagles last Sunday
Eli Manning threw a football in a tight spiral.
(a) If the ball spun at a rate of 550 rpm, what was its angular
velocity in rad/s?
(b) If it spun for 1.5 seconds before it was caught by Odell
Beckham Jr., how many radians did it rotate in total and how many
revolutions did it rotate in total? Assume there was no air
resistance.
2. Now let's consider a...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 11 minutes ago

asked 15 minutes ago

asked 15 minutes ago

asked 16 minutes ago

asked 16 minutes ago

asked 16 minutes ago

asked 26 minutes ago

asked 29 minutes ago

asked 38 minutes ago

asked 38 minutes ago

asked 39 minutes ago

asked 44 minutes ago