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?

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

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.

At t=3s, a point on the rim of a .2m radius wheel has a tangential speed of 50m/s as the wheel slows down with a tangential acceleration of constant magnitude 10m/s^2.
a) What is the constant angular acceleration?
b) What is the angular velocities at t=3s & t=0s
c) Through what angle did the wheel turn between t=0s & t=3s?

A ceiling fan has one red blade. Initially rotating in a counterclockwise (positive direction) with angular velocity Wo= +30 radians per second.
SEE THE ATTACHMENT FOR A PICTURE WITH KNOWN DATA.
At that instant, when the red blade makes an angle Qo= +1.4 radians from the +x axis, the current is reversed and a timer is started

A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s squared. Through what angle does the pulley turn in 5.26 s?