# Rotational Motion

##### Angular Kinematics
1. If a fan blade spins 5 times per second and it reaches this speed from rest in 3 seconds, what is the average angular acceleration of the blade?
2. If a blender rotates 80 times in a second what is its angular velocity? How far does it turn in 0.01 seconds?
3. The seconds hand on a clock takes 60 seconds to go around, what is its angular velocity? How about the minute hand?
4. You are pedaling a bicycle such that you give the wheel an angular acceleration of 0.15 rad/s².  If the wheel already has an angular velocity of 0.50rad/s how fast will it be rotating after 3 seconds?  How far will it have turned in that time?
5. If a wheel is spinning at 0.60 rad/s and then 3 rotations later it is spinning at 0.90 rad/s, what is the angular acceleration on the wheel?
##### Torque
1. If a 300N force is applied to a wheel 60cm from the axis and 30º away from being tangential, what is the torque from this force on the wheel?
2. If the torque exerted by a wrench is 10N·m when you pull it 10cm from the axis of rotation with a force of 200N, what angle is your force making with the wrench?
3. If two children are sitting on a seesaw one 1.5m from the axis of rotation and the other 2.5 meters from the axis of rotation and the first kid weighs 25kg and the second 15kg, what is the net torque on the seesaw?
4. If you push a disk with a force of 300N at the edge of the disk and tangential to it and the disk has a mass of 50kg and a radius of 0.40m, what will be the resulting angular acceleration of the disk?
5. If you hit a pool ball (mass=0.16kg, radius= 5.715cm) with a force of 250N at an angle of 45º from the ball’s surface what will be the torque on the ball? What will be the ball’s angular acceleration from this strike?
##### Rotational Energy
1. If you have a yoyo of mass 0.15kg and radius 3cm (shaped like a disk) and you let it unwind by gravity the full length of the string which is 1.5m, what will be its angular velocity at the end?
2. What is the rotational energy of a baseball bat (mass=0.96kg, length=106cm) treating it like a uniform rod rotating at one end, if the tip of the bat is moving at 30m/s?
3. You have a spring with spring constant, k=1000N/m, and it is compressed by 2.5m and touching a ring of mass 25kg and radius 0.60m.  If the spring is released so that it pushes the ring and the ring disconnects from the spring when it reaches its unstretched length, what will be the angular velocity of the ring if it rolls without slipping?
4. A hula hoop of mass 5.0kg and radius 0.80m is rolled up a hill without slipping at a speed of 5.0m/s. How far up the hill will it travel if the slope of the hill is 20º?
5. A person climbs into a garbage can and then is rolled down a hill changing elevation by 20m. If the person plus can has a mass of 75kg and the radius of the garbage can is 0.60m what will be the angular velocity of the can when it reaches the bottom of the hill if friction is negligible and the can rolls without slipping?
##### Angular Momentum
1. In the Olympics there is a sport called the discus throw where the athlete spins around and then uses their momentum to throw a disk.  If we can approximate the athlete as a cylinder with mass of 55kg and a radius of 0.5m and the discus has a mass of 2kg, what would the velocity of the discuss be if the athlete has a angular velocity of 3rad/s and comes to a complete stop when the discus is thrown?
2. Two rings are rotating in opposite directions. The first has a mass of 30kg and an angular velocity of 2.50rad/s. The second has a mass of 45kg and a angular velocity of 1.25rad/s.  The both have the same radius of 40.0cm.  If the two rings share a common axel, collide and stick to each other, what will be there angular velocity after they collide?
3. A 50kg rod is swinging around a pole attached at one end. The rod is 1.75m long and is rotating at 2.5rad/s.  If you apply a force 1.25m from the axis of rotation that brings the rod to a complete stop in 0.2seconds, what must be the magnitude of that force assuming it is perpendicular to the rod?
4. A baseball (mass=145g) is pitched so that it 0.35m from the center of a batter at a speed of 35m/s. What is the angular momentum of the baseball compared to the batter’s center? If the batter hits the ball so that it goes back in exactly the direction it came with the same speed, and the bat is in contact with the ball for 0.050s, what is the torque the batter exerts on the ball?
5. A steel pole hangs from a pivot 3.5m above it. The pole has a mass of 25kg. If a 35kg child running at a speed of 8m/s jumps on the end of the pole what will be the angular velocity of the pole and child?  How high will the child get off the ground before the pole starts coming back?