Question

A disk-shaped machine part has a diameter of 39.0 cm. Its angular position is given by...

A disk-shaped machine part has a diameter of 39.0 cm. Its angular position is given by

θ = −1.22t3 + 1.60t2,

where t is in seconds and θ is in radians.

(a) What is the maximum angular speed of the part during this time interval? (Assume the time interval is from t = 0 to when the part reverses its direction.)
rad/s

(b) What is the maximum tangential speed of a point halfway to the rim of the part during this time interval?
m/s

(c) What is the time t for which the part reverses its direction of motion after

t = 0?


s

(d) Through how many revolutions has the part turned when it reaches the time found in part (c)?
revolutions

Science   Physics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

a) given

then angular speed is

and angular acceleration is

a) Angular speed is maximum when a = 0

Therefore

or

b) diameter is d = 0.39 m

the maximum tangential speed of a point d/4 at t = 0.437 s is

c) the time for which the part reverses its direction of motion is when theta = 0

or

d) The total angular displacement during this time is

The number of revolutions is

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A 44.0-cm diameter disk rotates with a constant angular acceleration of 3.00 rad/s2. It starts from...
A 44.0-cm diameter disk rotates with a constant angular acceleration of 3.00 rad/s2. It starts from rest at t = 0, and a line drawn from the center of the disk to a point P on the rim of the disk makes an angle of 57.3° with the positive x-axis at this time. (a) At t = 2.48 s, find the angular speed of the wheel. rad/s (b) At t = 2.48 s, find the magnitude of the linear velocity...
During a certain time interval, the angular position of a swinging door is described by θ...
During a certain time interval, the angular position of a swinging door is described by θ = 4.96 + 10.7t + 1.93t2, where θ is in radians and t is in seconds. Determine the angular position, angular speed, and angular acceleration of the door at the following times. (a) t = 0 θ = rad ω = rad/s α = rad/s2 (b) t = 2.99 s θ =    rad ω =    rad/s α =    rad/s2
In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it....
In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it. The diameter of the roller is 4.00 m, and, while being driven into rotation around a fixed axis, its angular position is expressed as θ = 2.10t2 − 0.850t3 where θ is in radians and t is in seconds. (a) Find the maximum angular speed of the roller. rad/s (b) What is the maximum tangential speed of a point on the rim of the...
In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it....
In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it. The diameter of the roller is 9.00 m, and, while being driven into rotation around a fixed axis, its angular position is expressed as θ = 2.40t2 − 0.650t3 where θ is in radians and t is in seconds. (a) Find the maximum angular speed of the roller. rad/s (b) What is the maximum tangential speed of a point on the rim of the...
Frictional torque causes a disk to decelerate from an angular speed of 4.30 rad/s at t...
Frictional torque causes a disk to decelerate from an angular speed of 4.30 rad/s at t = 0 to 2.00 rad/s at t = 4.80 s. The equation describing the angular speed of the wheel during this time interval is given by dθ dt = ω0e−bt, where b and ω0 are constants. (a) What are the values of b and ω0 during this time interval? b = _______s−1 ω0 = _______rad/s (b) What is the magnitude of the angular acceleration...
A compact disk, which has a diameter of 12.0 cm, speeds up uniformly from zero to...
A compact disk, which has a diameter of 12.0 cm, speeds up uniformly from zero to 4.20 rev/s in 2.90s. (A) What is the tangential acceleration of a point on the outer rim of the disk at the moment when its angular speed is 2.00 rev/s ? (B) What is the tangential acceleration of a point on the outer rim of the disk at the moment when its angular speed is 3.00 rev/s?
The angular position of a point on the rim of a rotating wheel is given by...
The angular position of a point on the rim of a rotating wheel is given by ? = 6.0t - 2.0t2 + t3, where ? is in radians and t is in seconds. (a) What is the angular velocity at t = 2 s? rad/s (b)What is the angular velocity at t = 4.0 s? rad/s (c) What is the average angular acceleration for the time interval that begins at t = 2 s and ends at t = 4.0...
The angular position of a point on the rim of a rotating wheel is given by...
The angular position of a point on the rim of a rotating wheel is given by θ = 7.88t - 3.72t2 + 2.28t3, where θ is in radians and t is in seconds. What are the angular velocities at (a) t = 1.42 s and (b) t = 6.30 s? (c) What is the average angular acceleration for the time interval that begins at t = 1.42 s and ends at t = 6.30 s? What are the instantaneous angular...
The angular position of a point on the rim of a rotating wheel is given by...
The angular position of a point on the rim of a rotating wheel is given by θ = 1.82t - 5.66t2 + 3.63t3, where θ is in radians and t is in seconds. What are the angular velocities at (a) t = 1.17 s and (b) t = 7.69 s? (c) What is the average angular acceleration for the time interval that begins at t = 1.17 s and ends at t = 7.69 s? What are the instantaneous angular...
A .13 kg disk is rotating at an angular speed of 57 rad/s. The disk has...
A .13 kg disk is rotating at an angular speed of 57 rad/s. The disk has a radius of .25m. The disk speeds up for 3 s. After the 3 s have passed, the edge of the disk is under a centripetal forxe of 313.13 N. What is the centripetal acceleration of the disk at this time? What is the final angular velocity of the disk after the 3 s? What is the angular acceleration during the 3 s interval...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT