Rotational Kinematics of a disc

In summary, the disk with a radius of 0.34m and a mass of 7.4kg has an angular acceleration of 100.2 rad/s2. Using the formula for angular displacement, the angle turned after 1.3 seconds is 84.669 rad. To find the distance traveled, the circumference of the circle (2.136m) was multiplied by the angle turned and divided by 2π. The resulting distance was 28.783m, which may have a slight rounding error. The translational speed of the disk refers to its speed as it moves across the table and can be calculated using standard kinematics formulas.
  • #1
mattmannmf
172
0
How far has the disk moved?

Disk has .34m radius with a mass of 7.4. The angular acceleration about the center of mass is 100.2 rad/s2.

So this is what i did:
ang. disp= .5(ang. accel)*t^2
(x=.5(a)t^2 =>pretty much)

I got my ang. disp to be 84.669 rad. Now i need to convert it to meters.
The circum. of the circle i got was 2.136 (2(pi)r= 2*3.1415*.34). so that's how far it goes in 1 revolution.

So i do 84.669rad* (1 rev/(2(pi) rad) * (2.136 m/ 1 rev)... so (84.669*2.136)
/ (2(pi))

I got the answer to be 28.78 m...and when i checked it was wrong...no idea where i went wrong

Also the 2nd part of the question asks what is the translational speed of the disk... i have no idea what translational speed is or means. please help!
 
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  • #2
Were you given a value for time? Could you state the entire question as it was given to you?
 
  • #3
A solid uniform disk of mass M = 7.4 kg and radius R = 34 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 = 126 N is applied to the string. The string does not slip on the rim.

a) What is the acceleration of the center of mass?
a = m/s2 *
17.03 OK

HELP: Draw a free-body diagram and apply Newton's Second Law.

b) What is the angular acceleration about the center of mass?
a = rad/s2 *
100.2 OK

HELP: Draw a free-body diagram, find the torque, and apply the rotational analog of Newton's 2nd Law.

The next 5 questions refer to a time 1.3 s after the force is first applied.
c) How far has the disk moved?
d = m
28.783 NO

HELP: This is a problem in one-dimensional kinematics.
HELP: We have a constant acceleration, so we can use our standard kinematics formulas to find out the distance traveled in a given time.

d) Through what angle has the disk turned?
q = rad *
84.669 OK

e) What is the translational speed of the disk?
 
  • #4
The next 5 questions refer to a time 1.3 s after the force is first applied.
c) How far has the disk moved?
d = m
28.783 NO
I think you are missing a factor of two somewhere.

e) What is the translational speed of the disk?
Translation in this case just means as it moves across the table.
 
  • #5
missing a factor of 2? i don't know... like the math seems right. Maybe i am off by a little bit due to rounding error?
 
  • #6
yes..where I= .5*m*r^2
 

FAQ: Rotational Kinematics of a disc

What is rotational kinematics?

Rotational kinematics is the study of the motion of objects that rotate around a fixed axis. It involves analyzing the position, velocity, and acceleration of a rotating object.

How is rotational kinematics different from linear kinematics?

Rotational kinematics deals with the motion of objects that rotate, while linear kinematics deals with the motion of objects that move in a straight line. Rotational kinematics also takes into account the object's rotational inertia and angular velocity, while linear kinematics focuses on linear inertia and linear velocity.

What is the relationship between angular and linear velocity?

Angular velocity is the rate of change of an object's angular position, while linear velocity is the rate of change of its linear position. The two are related by the equation v = rω, where v is linear velocity, r is the distance from the axis of rotation to the object, and ω is angular velocity.

How is rotational kinematics applied in real life?

Rotational kinematics is applied in various fields such as engineering, physics, and sports. It is used to design and analyze rotating machinery, such as engines and turbines. In sports, rotational kinematics is used to improve techniques in activities like golf swings and gymnastics routines.

What factors affect the rotational kinematics of a disc?

The rotational kinematics of a disc is affected by factors such as the disc's mass, diameter, and shape. The distribution of mass also plays a role, as well as external forces acting on the disc, such as friction and air resistance.

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