A gyroscope slows from an initial rate of 32.0 rad/s at a rate of 0.700 rad/s$^2$ . (a) How long does it take to come to rest? (b) How many revolutions does it make before stopping?

At its peak, a tornado is 60.0 m in diameter and carries 500 km/h winds. What is its angular velocity in revolutions per second?

During a very quick stop, a car decelerates at 7.00 m/s$^2$ . (a) What is the angular acceleration of its 0.280-m-radius tires, assuming they do not slip on the pavement? (b) How many revolutions do the tires make before coming to rest, given their initial angular velocity is 95.0 rad/s ? (c) How long does the car take to stop completely? (d) What distance does the car travel in this time? (e) What was the car's initial velocity? (f) Do the values obtained seem reasonable, considering that this stop happens very quickly?

An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. (a) What is the average angular acceleration in rad/s²? (b) What is the tangential acceleration of a point 9.50 cm from the axis of rotation? (c) What is the centripetal acceleration in m/s² and multiples of g of this point at full rpm? (d) What is the total distance travelled by a point 9.5 cm from the axis of rotation of the ultracentrifuge?

During a very quick stop a car decelerates at $2.5\ {\rm{m/s^2}}$ during $1.7\ {\rm{s}}$. What is the distance traveled by the car in such time?

during a very quick stop a car decelerates at 7.00 m/s2. If the car was traveling at a speed of 100 m/s, how much distance did it travel after it started decelerating until it completely stopped?

Suppose a piece of dust finds itself on a CD. If the spin rate of the CD is 500 rpm, and the piece of dust is 4.3 cm from the center, what is the total distance traveled by the dust in 3 minutes? (Ignore accelerations due to getting the CD rotating.)

With the aid of a string, a gyroscope is accelerated from rest to 32 rad/s in 0.40 s under a constant angular acceleration. (a) What is its angular acceleration in rad/s²? (b) How many revolutions does it go through in the process?

A track star runs a 400-m race on a 400-m circular track in 45 s. What is his angular velocity assuming a constant speed?

A particle moves 3.0 m along a circle of radius 1.5 m. (a) Through what angle does it rotate? (b) If the particle makes this trip in 1.0 s at a constant speed, what is its angular velocity? (c) What is its acceleration?

An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. a. What is its angular acceleration in rad/s²? b.What is the tangential acceleration (in m/s²) of a point 10.00 cm from the axis of rotation? c. What is the radial acceleration in m/s²? and in multiples of g of this point at full rpm?

With the aid of a string, a gyroscope is accelerated from rest to 32 rad/s in 0.40 s. (a) What is its angular acceleration in rad/s$^2$? (b) How many revolutions does it go through in the process?

Everyday application: Suppose a yo-yo has a center shaft that has a 0.250 cm radius and that its string is being pulled. (a) If the string is stationary and the yo-yo accelerates away from it at a rate of 1.50 m/s$^2$ , what is the angular acceleration of the yo-yo? (b) What is the angular velocity after 0.750 s if it starts from rest? (c) The outside radius of the yo-yo is 3.50 cm. What is the tangential acceleration of a point on its edge?

A wheel rotates at a constant rate of 2.0 × 10³ rev/min. (a) What is its angular velocity in radians per second? (b) Through what angle does it turn in 10 s? Express the solution in radians and degrees.