A bar on a hinge starts from rest and rotates with an angular acceleration a = 10 + 6t, where a is in rad/s2 and t is in seconds. Determine the angle in radians through which the bar turns in the first 4.00 s.

A dentist's drill starts from rest. After 4.30 s of constant angular acceleration it turns at a rate of 2.05 ✕ 104 rev/min. (a) Find the drill's angular acceleration. rad/s2(b) Determine the angle (in radians) through which the drill rotates during this period.

An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: θ(t) = a + bt2 – ct3 where a = 2.1 rad, b = 0.75 rad/s2 and c = 0.035 rad/s3. a. Determine an equation for the angular speed of the ride as a function of time, omega(t). Write your answet using the symbols a, b, and c, instead of their numerical values. b. Besides at t = 0, at what time t1 is the ride stopped? Give your answer in seconds. c. What is the magnitude of the angular displacement of the ride in radians between times t = 0 and t = t1? d. Determine an equation for the angular acceleration of the ride as a function of time, alpha(t). Write your answer using the symbols a, b, and c, instead of their numerical values.  e. What is the angular acceleration in rad/s^2 when the ride is at rest t = t1?

A boy rides his bicycle 1.68 km. The wheels have a radius 32.5 cm. What is the total angle (in rad) the tires rotate through during his trip?

An electric motor rotating a workshop grinding wheel at a rate of 151rev/min is switched off. Assume constant angular deceleration of magnitude 2.93 rad/s2. Through how many revolutions does the wheel turn before it finally comes to rest?

Convert 51.0° to radians.  rad (b) Convert 17.0 rad to revolutions.  rev (c) Convert 79.0 rpm to rad/s.  rad/s

A dentist's drill starts from rest. After 3.30 s of constant angular acceleration it turns at a rate of 2.10 x 10° rev/min. (a) Find the drill's angular acceleration. | rad/s² (b) Determine the angle (in radians) through which the drill rotates during this period. rad

Starting from rest, a wheel undergoes a constant acceleration for 10 seconds. When t = 3.0 s, the angular velocity of the wheel is 6.0 rad/s. Find the total angle the wheel rotates from t = 0 to t = 20 s.

The angular speed of a wheel decreases uniformly from 34.0 rad/s to 2.0 rad/s in 18.0 s.A. Find the constant angular acceleration in rad/s^2.B. Find the number of revolutions made by the wheel in this time.

A helicopter propeller blade starts from rest and experiences a constant angular acceleration of 25.0 rad/s2. Find the speed of a point on the blade 2.70 m from the axis of rotation when the blade has completed 20 revolutions