Angular speeds in radians, linear speeds and average angular acceleration.

A pneumatic high-speed cutter with a 7.50 cm diameter cutting disc is advertised to have a rotationrate of between 5,000 and 18,000 rev/min.

A) What is the range of angular speeds in radians?
B) What is the range of linear speeds of the edge of the disk?
C) What is the average angular acceleration if, starting from rest, the cutter comes up to its fastest speed in 2.8 seconds?

Solution Summary

with good explanations and calculations, the problem is solved.

A 5.0-m-diameter merry-go-round is initially turning with a 4.0 s period. It slows down and stops in 20 s.
a) Before slowing, what is the speed of a child on the rim? (in m/s)
b) How many revolutions does the merry-go-round make as it stops?

A certain CD has a playing time of 78 minutes. When the music starts, the CD is rotating at an angular speed of 4.8 * 10^2 revolutions per minute (rpm). At the end of the music, the CD is rotating at 2.1 * 10^2 rpm. Find the magnitude of the averageangular acceleration of the CD. Express your answer in rad/s2.

Could you please provide the answers and workings out to the following physics problems.
1. A wheel with a 0.10-m radius is rotating at 35 rev/s. It then slows uniformly to 15 rev/s over 3.0-s interval. What is the angular acceleration of a point on the wheel?
2. During the spin-dry cycle of a washing machine, the motor slo

On a reel-to-tape deck, the tape is pulled past the playback head at a constant linear speed of 0.381 m/s.
A) Using the data in part a of the drawing, find the angular speed of the take-up reel.
B) After 2.40 x 10^3 s, the take-up reel is almost full. Find the averageangular acceleration of the reel and specify whether

Question: The blades of a fan running at low speed turn at 250 rpm. When the fan is switched to high speed, the rotation rate increases uniformly to 350 rpm in 5.75 s.
a.) What is the magnitude of the angular acceleration of the blades?
b.) How many revolutions do the blades go through while the fan is accelerating?

Question: The blades in a blender rotate at a rate of 7290 rpm. When the motor is turned off during operation, the blades slow to rest in 3.67 s. What is the angular acceleration as the blades slow down? The initial rotation is in the positive direction.

A wheel that is rotating at 33.3 rad/s is given an angular acceleration of 2.15 rad/s/s. Through what angle has the wheel turned when its angular speed reaches 72.0 rad/s?

Q: "The blades in a blender rotate at a rate of 7290 rpm. When the motor is turned off during operation, the blades slow to rest in 3.67 s. What is the angular acceleration as the blades slow down? The initial rotation is in the positive direction."
The OTA's solution is attached. We both got an answer of 208 rad/s^2.