Calculating Torque for LP Turntable with Given Angular Speed and Mass

In summary, to play a record on an LP turntable, the motor must deliver enough torque to reach a final angular speed of 3.53 rad/s. To find the required torque, we need to calculate the angular acceleration, which can be found using the equations T=rF, F=ma, and Theta=(angular acceleration * t^2)/2. However, as the time is not given in the problem, we can use the average speed of the turntable while it's accelerating to calculate the time. The average speed can be calculated using the distance (converted from revolutions to radians) and the given final speed.
  • #1
cstout
37
0

Homework Statement



An LP turntable must spin at 3.53 rad/s to play a record. How much torque must the motor deliver if the turntable is to reach its final angular speed in 1.9 revolutions, starting from rest? The turntable is a uniform disk of diameter 30.7 cm and mass 0.24 kg.

Homework Equations



T=rF
F=ma
Theda = (Angular Acceleration (t^2)) / 2

The Attempt at a Solution



I tried using the above equations but I'm not sure about finding the angular acceleration to find the the final Torque.
 
Physics news on Phys.org
  • #2
What's the most basic definition of acceleration? That's what you need here.
 
  • #3
change in distance / change in time
 
  • #4
cstout said:
change in distance / change in time
That's the definition of velocity. What's the similar definition of acceleration?
 
  • #5
oh yea, sorry, change in velocity / change in time
 
  • #6
cstout said:
oh yea, sorry, change in velocity / change in time
Good. So the angular acceleration is the change in angular velocity over time.

But I just realized that they didn't give you the time--I misread the problem. (D'oh!) So you'll need to use another approach to find the time.

Try this: What's the average speed of the turntable while it's accelerating? Use that--and the distance--to calculate the time. (Change revolutions to radians.)
 
  • #7
Ok, so the Time = Distance / Average Speed, the distance is 11.932 radians, but what is the average speed, is it simply the given speed of 3.53 or something else?
 
  • #8
cstout said:
but what is the average speed, is it simply the given speed of 3.53 or something else?
No. 3.53 rad/s is the final speed and 0 is the initial speed. So what's the average speed?
 

1. What is torque and how does it relate to angular speed?

Torque is the measure of the force that causes an object to rotate around an axis. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation. Angular speed, on the other hand, is the rate at which an object rotates around an axis. Torque and angular speed are directly related, as an increase in torque will result in an increase in angular speed.

2. How is torque and angular speed different from linear speed?

Linear speed is the rate at which an object moves in a straight line, while angular speed is the rate at which an object rotates around an axis. They are both measures of how fast an object is moving, but they describe different types of motion.

3. What is the unit of measurement for torque and angular speed?

Torque is typically measured in Newton-meters (N*m), while angular speed is measured in radians per second (rad/s). However, they can also be measured in other units such as foot-pounds (ft-lb) or revolutions per minute (rpm).

4. How does the direction of torque affect the direction of angular speed?

The direction of torque and angular speed are always the same. If the torque is applied in a clockwise direction, the object will rotate in a clockwise direction, and vice versa. This is known as the right-hand rule, where the direction of the fingers curled around the axis of rotation represents the direction of the torque and angular speed.

5. What factors affect the magnitude of torque and angular speed?

The magnitude of torque is affected by the magnitude of the force applied and the distance from the axis of rotation. The greater the force and the larger the distance, the greater the torque will be. For angular speed, the moment of inertia, or the resistance of an object to change its rotational motion, also plays a role. Objects with a higher moment of inertia will have a lower angular speed for the same amount of torque applied.

Similar threads

Calculating Final Angular Velocity of Turntable with Runner on a Horizontal Axis
    • Introductory Physics Homework Help
Replies
5
Views
3K
Applied torque/angular momemtum
    • Introductory Physics Homework Help
Replies
2
Views
2K
Angular Momentum, Inertia and Kinetic Energy?
    • Introductory Physics Homework Help
Replies
5
Views
2K
Conservation of Angular Momentum in a Rotating System
    • Introductory Physics Homework Help
Replies
1
Views
945
Simple Ice Skater with Conservation of Angular Momentum
    • Introductory Physics Homework Help
Replies
4
Views
1K
Speed of cylinder rolling along a horizontal surface gathering snow (Solved)
    • Introductory Physics Homework Help
Replies
13
Views
898
Coin on a turntable problem in a noninertial frame
    • Introductory Physics Homework Help
Replies
12
Views
2K
Time required for disk to reach angular speed?
    • Introductory Physics Homework Help
Replies
11
Views
2K
Torque and Initial Angular Velocity effect on time
    • Introductory Physics Homework Help
Replies
6
Views
1K
How to calculate angular speed?
    • Introductory Physics Homework Help
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top