Calculus problem with average angular velocity

Click For Summary
To find the average angular velocity from theta = 4 radians to theta = 9 radians, the total change in angular position is 5 radians. The time taken to reach these positions can be calculated by integrating the angular velocity function, which is .72t. The average angular velocity is determined by dividing the total change in angular position by the total time taken. After performing the calculations, the average angular velocity is confirmed to be 3 radians per second. The solution demonstrates the application of calculus in determining average rates of change in angular motion.
achiu17
Messages
4
Reaction score
0
A wheel has angular position theta = 0 (radians) at t = 0 (seconds). It then rotates with an angular velocity equal to .72t radians/sec. In radians per second, what is the average angular velocity from theta = 4 radians to theta = 9 radians?

I got 3 for my answer but I'm not sure if it's right
 
Physics news on Phys.org
Please post your working.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Integral for the linear speed of the Earth
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad How can angular displacement be larger than 2pi?
  • · Replies 20 ·
Replies
20
Views
2K
Undergrad Confusion about adding angular velocities
  • · Replies 4 ·
Replies
4
Views
2K
Angular velocity- A toy train rolls around a horizontal track
  • · Replies 8 ·
Replies
8
Views
914
How should I use the averaging approximation to find this?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad I'm calculating more energy out than I put in
  • · Replies 138 ·
5
Replies
138
Views
8K
Calculate the Angular Velocity of an Arm from a Data Set
  • · Replies 4 ·
Replies
4
Views
9K
Angular Velocity of a Car going around a curve
  • · Replies 9 ·
Replies
9
Views
1K
Brownian Ratchet (exercise framed by Feynman's Lectures, l. 46)
  • · Replies 32 ·
2
Replies
32
Views
2K
Change in Angular Velocity While Orbiting With No Torque
  • · Replies 30 ·
2
Replies
30
Views
3K