Rotational dynamics question 2

In summary, the conversation discusses the calculation of various quantities related to a string wrapped around a hoop. These include the acceleration of the hoop's center of mass, the tension in the string while descending, the time it takes to descend a certain distance, the speed of the center of mass, and the angular speed of the rotating hoop. The acceleration is found to be 4.9 m/s^2, the tension is 0.745 N, and the time, speed, and angular speed are calculated to be 0.495 s, 2.426 m/s, and 35.152 rad/s, respectively.
  • #1
squintyeyes
45
0
how do you do part c, d, and e

A string is wrapped several times around the rim of a small hoop of radius 0.0690 m and a mass 0.152 kg. The situation is sketched in the figure below.

If the free end of the string is held in place and the hoop is released from rest, calculate the following quantities:

(a) the magnitude of the acceleration of the hoop's center of mass
4.9 m/s2

(b) the tension in the string while the hoop descends and the string unwinds
0.745 N

(c) the time it takes the hoop to descend 0.600 m
_________ s

(d) the speed of the hoop's center of mass after it's descended 0.600 m
__________m/s

(e) the angular speed of the rotating hoop after it's descended 0.600 m
__________rad/s


Attempt
Σ Forces in x direction = ma
mg - Tension = ma
mg - T= ma

Σ Torque = Iα
Iα = Tr
(mr^2)(a/r)= Tr
T= ma

mg - T = ma
mg- ma = ma
mg = 2ma
g = 2a
a = g/2 = 9.8/2= 4.9

T = ma
= (0.152)(4.9)
= 0.7448
 

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  • #2
squintyeyes said:
how do you do part c, d, and e
You found the acceleration; use kinematics to solve those parts of the problem.
 
  • #3
so for part c, would i just do

Δy = vt + (1/2)at^2
0.6 = 0 + (1/2) (4.9) t^2
t^2 = 0.244897
t = 0.495 s

then d is found by

final velocity = inital velocity + at
= 0 + (4.9)(0.495)
= 2.426 m/s

Lastly e is found by

σ = v/r
= 2.426/0.069
= 35.152 rad/s

thanks i already put entered them and they are correct!
 
Last edited:

Related to Rotational dynamics question 2

1. What is rotational dynamics?

Rotational dynamics is the branch of physics that deals with the motion of objects that are rotating around a fixed axis. It involves the study of torque, angular velocity, and angular acceleration.

2. How is rotational dynamics different from linear dynamics?

Linear dynamics deals with the motion of objects in a straight line, while rotational dynamics deals with the motion of objects around a fixed axis. They both involve the study of forces and motion, but rotational dynamics also takes into account the rotational properties of an object.

3. What is torque and how is it related to rotational dynamics?

Torque is the measure of a force's ability to cause rotational motion. In rotational dynamics, torque is an important concept as it determines the rotational acceleration of an object.

4. Can you explain the concept of moment of inertia in rotational dynamics?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass and distribution of mass of an object. In rotational dynamics, moment of inertia is used to calculate an object's rotational kinetic energy.

5. How is rotational dynamics applied in real-life situations?

Rotational dynamics is applied in various real-life situations, such as the motion of objects like wheels, gears, and pendulums. It is also used in sports, such as in the movement of a baseball after it is thrown, or in the rotation of a figure skater during a spin. Understanding rotational dynamics is also important in designing and building machines and structures that involve rotational motion.

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