A high-speed sander has a disk 4.10cm in radius that rotates about its axis at a constant rate of 1250 revolutions per minute. a) Determine the angular speed of the disk in radians per second. b) Determine the linear speed of a point 1.80cm from the disk's center c) Determine the centripetal acceleration of a point on the rim. d) Determine the total distance traveled by a point on the rim in 1.80s.

The earth spins on its axis once a day and orbits the sun once a year. Determine the average angular velocity of the earth as it spins on its axis and orbits the sun. In each case take the positive direction for the angular displacement to be the direction of the earths motion

An electric fan is turned off, and its angular velocity decreases uniformly from 450 rev/min to 220 rev/min in a time interval of length 4.50s.  a) Find the angular acceleration α in revolutions per second per second.  b) Find the number of revolutions made by the fan blades during the time that they are slowing down in Part A.  c) How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in Part A?

5. A particle is moving along a circular path of radius 1.5 m and has an angular velocity of 10 rads/s. What is the particle's radial acceleration? What is the particle's tangential velocity?

Problem 12: A merry-go-round is a playground ride that consists of a large disk mounted to that it can freely rotate in a horizontal plane. The merry-go-round shown is initially at rest, has a radius R = 1.3 meters, and a mass M = 241 kg. A small boy of mass m = 46 kg runs tangentially to the merry-go-round at a speed of v = 1.8 m/s, and jumps on. Randomized Variables R = 1.3 meters M = 241 kg m = 46 kg v = 1.8 m/s

A truck with 0.420 m radius tires travels at 42 m/s. part a) What is the angular velocity of the rotating tires in radians per second?  part b) What is the angular velocity of the rotating tires in rev/min?

The wheel of an 80 cm diameter bicycle rotates at 50 rpm the moment a cyclist sees a pedestrian crossing. It applies the brake and comes to a complete stop 3 seconds later with constant deceleration during that period. Calculatea) The angular acceleration of the break.b) The number of turns made in 3 seconds.c) The angular velocity, period and frequency when the movement is UCM.d) Draw the velocity vector, the tangential acceleration vector and the normal acceleration vector for a point on the tire during braking.

LAA-2 A solid disk of radius 15.0cm starts at rest and reaches a final angular speed of 1,200rev/min clockwise after turning thru a total of 80.0 revolutions. rotation a) Find the (constant) angular acceleration of the disk in units of radians and seconds. b) Find the final linear speed in m/s of point P on the rim of the disk. c) Find the magnitude of the tangential acceleration of point P on the rim of the disk. point P R=15.0cm d) Find the magnitude of the radial acceleration of point P on the rim of the disk. e) Sketch on your paper a figure like the one to the right and show arrows that represents atan and arad at point P. 9:47 PM 梦 0 arch 66°F Mostly cloudy 9/23/2021 Gup ISTRUCTION

A figure skater does a single-axle jump, turning 1.5 revolutions while in the air. The skater is in the air for 0.48 s, and his hands are located 0.69 m from the rotation axis. a) What is the angular velocity (in rad/s) of the skater during the leap? b) What is the linear tangential speed (in m/s) of the skater's hand? c) What is the centripetal acceleration (in m/s^2) of each of the skater's hands during the jump?

3. A car is traveling on a circular race track of radius R=300 ft. and is being tracked by a device located at the center of the track which can rotate and measure the angular velocity of the vector locating the car (treated as a particle). If the car's speed is 150 ft/s and is increasing at a rate of 15 ft/s?, what is the angular rotational speed of the vector tracking the car. What is the magnitude of the acceleration of the car. de/dt S.G0 402E 1,051- 629 R.