01) The rotating arm starts from rest and acquires a rotational speed N= 200 rpm in 2 seconds with constant angular acceleration. Find the time t after starting before the acceleration vector of end P makes an angle of 45 with the arm OP. 0.5 m P

7. Find the tangential and normal components of acceleration for r(t) = (8 cos t ,8 sin t, 8t)

A student holds a bike wheel and starts it spinning with an initial angular speed of 9.0 rotations per second. The wheel is subject to some friction, so it gradually slows down. In the 10.0 s period following the inital spin, the bike wheel undergoes 77.5 complete rotations. Assuming the frictional torque remains constant, how much more time At, will it take the bike wheel to come to a complete stop? Ats = %3D S

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18 of 25 During the spin cycle of your clothes washer, the tub rotates at a steady angular velocity of 38.3 rad/s. Find the angular displacement A0 of the tub during a spin of 81.7 s, expressed both in radians and in revolutions. rad AO = revolutions AO =

When a fan is turned off, its angular speed decreases from 168 rpm to 64.0 rpm in 6.08 s.  A) what is the angukar acceleration of the fan? B) How fast the edges of the blades are moving (in m/s) at time 6.08 s, if they are 86.0 cm long?

3) Throwing: A hammer thrower spins 4 times in 1.6 s before releasing the hammer. The radius between the hammer centre of mass and the axis of rotation is 1.80 m. a. What is the average angular velocity of rotation in rad/s? b. What is the tangential linear velocity of the hammer at release? Please report your answers to 2 decimal places and in SI units. a. Answer: Unit: b. Answer: Unit:

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

During a very quick stop, a car decelerates at 7.69m/s?. a) What is the angular acceleration of its 0.195-m-radius tires, assuming they do not slip on the pavement? rad/s? b) How many revolutions do the tires make before coming to rest, given their initial angular velocity is 89 rad/s? rev 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? m/s