The angular position of a point on the rim of a rotating wheel is given by 0 = 3.07t - 3.28t2+ 3.19t³, where e is in radians and t is in seconds. What are the angular velocities at (a) t = 3.52 s and (b) t = 9.55 s? (c) What is the average angular acceleration for the time interval that begins at t = 3.52 s and ends at t = 9.55 s? What are the instantaneous angular accelerations at (d) the beginning and (e) the end of this time interval?

The angular speed of a rotating platform changes from ω0 = 3.6 rad/s to ω = 6.4 rad/s at a constant rate as the platform moves through an angle Δθ = 5.5 radians. The platform has a radius of R = 12 cm. Calculate the angular acceleration of the platform α in rad/s2.

The angular speed of a rotating platform changes from ω0 = 2.6 rad/s to ω = 8.8 rad/s at a constant rate as the platform moves through an angle Δθ = 4.5 radians. The platform has a radius of R = 44 cm. Calculate the angular acceleration of the platform α in rad/s2.

A ball of radius 0.200 m rolls with a constant linear speed of 3.35 m/s along a horizontal table. The ball rolls off the edge and falls a vertical distance of 1.80 m before hitting the floor. What is the angular displacement of the ball while the ball is in the air?

Starting from rest, a wheel with a radius of 0.39 m begins to roll across the ground in a straight line under a constant angular acceleration of 5 rad/s2. What is the speed of the wheel in m/s after it has rotated through 14.8 full revolutions?

A motorsports driver is driving his car at a constant speed of 37.0 m/s on a circular track with a radius of 260 m. What is the angular speed (in rad/s) of the car? What are the magnitude (in m/s2) and direction of the car's acceleration?

Starting from rest, a wheel with a radius of 0.6 m begins to roll across the ground in a straight line under a constant angular acceleration of 4.43 rad/s2. What is the speed of the wheel in m/s after it has rotated through 17 full revolutions?

Starting from rest, a wheel with a radius of 0.58 m begins to roll across the ground in a straight line under a constant angular acceleration of 4.74 rad/s2. What is the speed of the wheel in m/s after it has rotated through 16 full revolutions?

The blades in a blender rotate at a rate of 6200 rpmrpm . When the motor is turned off during operation, the blades slow to rest in 2.6 s.  What is the angular acceleration as the blades slow down?

A wind turbine rotates at 15.8 rpm and has an angular acceleration of 0.0502 rad/s2. If the wind turbine takes 33.0 s to come to a complete stop, how many revolutions will this take?