Question

In: Physics

A child's spinning top is wound with a string. The top has a moment of inertia...

A child's spinning top is wound with a string. The top has a moment of inertia equal to 12.3 kg m2.  The string applies a tangential force of 456 N, at a radius of 3.00 cm. The string is wound around the top 8 times, which makes the top rotate through 8 full rotations while the string is being pulled.

a) What is the speed of the top just after the string is pulled?

b) What is its kinetic energy?

Solutions

Expert Solution

Moment of inertia of the top = I = 12.3 kg.m2

Tangential force applied by the string = T = 456 N

Radius at which the tangential force is applied = R = 3 cm = 0.03 m

Angular acceleration of the top =

= 11.122 rad/s2

Number of revolutions made by the top = n = 8

Angle through which the top rotates =

= 50.265 rad

Initial angular speed of the top = 1 = 0 rad/s

Final angular speed of the top = 2

2 = 33.44 rad/s

Final kinetic energy of the top = E

E = 6.88 x 103 J

a) Speed of the top just after the string is pulled = 33.44 rad/s

b) Kinetic energy of the top = 6.88 x 103 J


Related Solutions

We will find the Moment of Inertia Moment and Polar Moment of Inertia of a U...
We will find the Moment of Inertia Moment and Polar Moment of Inertia of a U profile that will determine its dimensions by ourselves.
8. A rigid object with moment of inertia 25 Kg m^2 is spinning around a fixed...
8. A rigid object with moment of inertia 25 Kg m^2 is spinning around a fixed axis with angular speed of 10 rad/s. A constant torque of 50 Nm is applied in a direction that slows down the rotation, for 2 seconds. (i) Calculate the angular speed of the object at t = 5 s. (ii) Calculate the kinetic energy of the object at t = 5 s. 9.A disc of moment of inertia 10 kg m^2 about its center...
A very light string is wound around a cylindrical spool of inertia M and radius R....
A very light string is wound around a cylindrical spool of inertia M and radius R. The cylinder rotates on a frictionless horizontal axis with a moment of inertia 1 2MR2 . Attached to the end of the string is a block of inertia m, which pulls on the string and unwinds it from the cylinder, as the block falls. (a)Draw an extended free-body diagram for the cylinder, and a regular free-body diagram for the block. (b)Let m = 5...
String is wrapped around an object of mass M = 0.3 kg and moment of inertia...
String is wrapped around an object of mass M = 0.3 kg and moment of inertia I = 0.01 kg·m2. You pull the string with your hand straight up with some constant force F such that the center of the object does not move up or down, but the object spins faster and faster (see the figure). This is like a yo-yo; nothing but the vertical string touches the object. When your hand is a height y0 = 0.26 m...
How would a spinning disk's kinetic energy change if its moment of inertia were five times...
How would a spinning disk's kinetic energy change if its moment of inertia were five times larger but its angular speed were five times smaller?  0.1 times as large as before  10 times as large as before  5 times as large as before  same as before  0.2 times as large as before
To calculate moment of inertia
To calculate moment of inertia of axis passing through centre of a square 
moment of inertia of a rod
Starting with the formula for the moment of inertia of a rod rotated around an axis through one end perpendicular to its length (I=M ℓ² / 3), prove that the moment of inertia of a rod rotated about an axis through its center perpendicular to its length is I=M ℓ² / 12. You will find the graphics in Figure 10.12 useful in visualizing these rotations.  
Moment of inertia for equilateral triangle
Three rods each of mass m and length I are joined together to form an equilateral triangle as shown in figure. Find the moment of inertia of the system about an axis passing through its centre of mass and perpendicular to the plane of triangle.
A toy top with a spool of diameter 5.0cm has a moment of inertia of 3.0x10^-5kg x m^2 about its rotation axis.
A toy top with a spool of diameter 5.0cm has a moment of inertia of 3.0x10^-5kg x m^2 about its rotation axis. To get the top spinning, its string is pulled with a tension of .30 N. How long does it take for the top to complete the first five revolutions? The string is long enough that it is wrapped around the top more than five turns
Calculate moment of inertia of disc with remaining portion
From a uniform circular disc of radius R and mass 9 M, a small disc of radius R/3 is removed as . Calculate the moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through the centre of the disc.  
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT