Rotational Kinematics
A wheel accelerates from 2 rad/s to 14 rad/s in 5 seconds. What is the angular acceleration?
2.4 rad/s2
What is the torque on a bolt produced by a 15-N force exerted perpendicular to a wrench that is 25 cm long?
3.75 N m
Which is more resistant to move: a solid cylinder or a hollow cylinder?
A hollow cylinder -- mass is a greater average distance from the axis of rotation.
Explain how holding a long pole increases a tightrope walker's stability?
A bike wheel is rotating 18 rad/s. It accelerates at a rate of 3 rad/s2. How long does it take until the wheel is rotating at 30 rad/s?
4 seconds
A bolt on a car engine must be tightened with a torque of 35 Nm. You use a 25 cm wrench and pull at an angle of 60ยบ to the handle. How much force must you exert?
161.66 N
A hoop has a rotational inertia of 0.02 kgm2. If the net torque acting on the hoop is 0.3 Nm, what is the angular acceleration?
15 rad/s2
You are using a rod as a lever to move a large rock. Is it more effective to place the fulcrum nearer to your hands or the rock?
The rock. A longer lever arm gives you more torque and ability to move the rock.
Someone holds a frisbee in their hand. They throw it, setting it into rotational motion. If it accelerates at 6 rad/s2, how many radians does it rotate in 3 seconds?
27 radians
A 1.2 kg mass is hanging 0.2 m from the fulcrum on a 0.8 m rod. If the rod is balanced, how far from the fulcrum is the 2 kg weight hanging on the other side?
0.12 m
A ball is kicked with a net torque of 19 Nm. If the ball's angular acceleration is 6 rad/s2, what is the rotational inertia of the ball?
3.17 kgm2
A child moves from the center of the merry-go-round to the outer edge. Will the rotational velocity of the ride increase, decrease, or remain constant?
Velocity will decrease because the inertia increases when the average distance of mass increases but the angular momentum stays the same. L = Iw
A potter's wheel rotates 3 rad/s initially and increases to 5 rad/s. If the wheel covers 6.8 radians as it speeds up, what rate was it accelerating?
1.18 rad/s2
A 8 m long wooden plank rests on a fulcrum 3 m from the right end. If the wooden plank has a mass of 20 kg, how far from the fulcrum should a 40 kg child sit?
0.5 m
A spinning top has a rotational inertia of 2 kgm2. If the top is rotating at 8 rad/s, what is its angular momentum?
16 kgm2/s
Most speedometers measure the angular velocity of the transmission and convert it to speed. How will increasing the diameter of the tires affect the reading of the speedometer?
No change -- angular velocity is not based on radius of the object.
A washing machine's two spin cycles are 328 rev/min and 542 rev/min. What is the difference in angular velocities?
22.4 rad/s
Two men fight over the steering wheel in a car heist. Suppose the driver pulls the wheel tangentially counterclockwise with a force of 42 N. The passenger pulls tangentially on the wheel with a force of 35 N clockwise. If the radius of the steering wheel is 20 cm, what is the net torque on the wheel and in what direction does it turn?
1.4 Nm counterclockwise
A child spins on a chair with his arms out. His rotational inertia is 8 kgm2 and he rotates 3 rad/s. When he brings his arms in his rotational inertia decreases to 5 kgm2. What is his new angular speed?
4.8 rad/s
Your pet hamster sits on a record player whose angular speed is constant. If he moves to a point twice as far from the center, then his linear speed...
doubles.