DATA You are analyzing the motion of a large flywheel that has radius 0.800 m. In one test run, the wheel starts from rest and turns with constant angular acceleration . An accelerometer on the rim of the flywheel measures the magnitude of the resultant acceleration a of a point on the rim of the flywheel as a function of the angle θ – θ 0 through which the wheel has turned. You collect these results: Construct a graph of a 2 (in m 2 /s 4 ) versus ( θ – θ 0 ) 2 in (rad 2 ). (a) What are the slope and y -intercept of the straight line that gives the best fit to the data? (b) Use the slope from part (a) to find the angular acceleration of the flywheel, (c) What is the linear speed of a point on the rim of the flywheel when the wheel has turned through an angle of 135°? (d) When the flywheel has turned through an angle of 90.0°, what is the angle between the linear velocity of a point on its rim and the resultant acceleration of that point?
DATA You are analyzing the motion of a large flywheel that has radius 0.800 m. In one test run, the wheel starts from rest and turns with constant angular acceleration . An accelerometer on the rim of the flywheel measures the magnitude of the resultant acceleration a of a point on the rim of the flywheel as a function of the angle θ – θ 0 through which the wheel has turned. You collect these results: Construct a graph of a 2 (in m 2 /s 4 ) versus ( θ – θ 0 ) 2 in (rad 2 ). (a) What are the slope and y -intercept of the straight line that gives the best fit to the data? (b) Use the slope from part (a) to find the angular acceleration of the flywheel, (c) What is the linear speed of a point on the rim of the flywheel when the wheel has turned through an angle of 135°? (d) When the flywheel has turned through an angle of 90.0°, what is the angle between the linear velocity of a point on its rim and the resultant acceleration of that point?
DATA You are analyzing the motion of a large flywheel that has radius 0.800 m. In one test run, the wheel starts from rest and turns with constant angular acceleration. An accelerometer on the rim of the flywheel measures the magnitude of the resultant acceleration a of a point on the rim of the flywheel as a function of the angle θ – θ0 through which the wheel has turned. You collect these results:
Construct a graph of a2 (in m2/s4) versus (θ – θ0)2 in (rad2). (a) What are the slope and y-intercept of the straight line that gives the best fit to the data? (b) Use the slope from part (a) to find the angular acceleration of the flywheel, (c) What is the linear speed of a point on the rim of the flywheel when the wheel has turned through an angle of 135°? (d) When the flywheel has turned through an angle of 90.0°, what is the angle between the linear velocity of a point on its rim and the resultant acceleration of that point?
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
A wheel rotates through an angle of 324° as it slows down from 87.4 rpm to 18.7 rpm (revolutions per minute).
What is the magnitude of the average angular acceleration of the wheel in rad/s2?
A pottery wheel spins counter-clockwise with an initial angular speed of 68.7 rpm, as a potter sculpts a clay vase. The potter pushes on the pedal to apply an acceleration of 6.81 rad/s2, and the wheel steadily speeds up to a top angular speed 140 rpm. Use radians as the standard unit for angles.
A disk of radius 2.25 m rotates about its axis. Points on the rim of the disk undergo tangential acceleration of magnitude
1.81 m/s?. At a particular time, the rim has a tangential speed of 1.67 m/s. At a time 0.867 s later, what is the tangential
speed v of a point on the rim, the magnitude of the point's radial acceleration a,, and the magnitude of its total acceleration
Arot?
U =
m/s
ar =
m/s?
Atot =
m/s?
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