Describing Motion
What does rad/s mean?
Radians per second (aka angular velocity)
What is torque?
The combination of force and lever arm that can cause an object to rotate; the magnitude is equal to the force times the perpendicular lever arm.
Descirbe the moment of inertia.
An object's resistance to changes in rotation
It takes 108 Nm of torque to turn a lug nut at a 60 degree angle with a .2 meter wrench. Determine the force you need to apply.
623.53 N
A 0.5-meter diameter bicycle wheel is rotating at 6.28 or 2π rad/s. What is the linear velocity in m/s of a point on the rim of the wheel?
1.57 m/s
Determine the angular velocity (ω) in radians per second for an hour hand on a clock.
1.45 x 10-4 rad/s
You stand on a bicycle pedal and push straight down. Your mass is 65 kg. If the pedal makes an angle of 35° above the horizontal and the pedal is 18 cm from the center of the chain ring. Determine how much torque you exert.
65.76 Nm
A hula-hoop has a mass of 0.35 kg and a diameter of 1.5 m. Determine its moment of Inertia.
0.196 kgm2
An object has an angular acceleration of 4.5 rad/s2 and a radius of 0.5 m. Determine the force needed to be applied if the moment of inertia is 2.3 kgm2 (assume the force is applied at a 90 degree angle).
20.7 N
Determine the torque produced by a 75 N perpendicular force at the end of a 0.2 m long wrench.
15 Nm
A fan that is turning at 10 rad/s speeds up to 25 rad/s in 10 seconds. Determine the angular acceleration.
1.5 rad/s2
A bolt is to be tightened with a torque of 8.0 Nm. If you have a wrench that is 0.35 m long, what is the least amount of force you must exert?
22.85 N
A stone-age wheel has a mass of 25kg and a radius of .89 m. Determine the wheel's moment of inertia.
9.9 kgm2
The torques are of two children on a seesaw are at perfect equilibrium. One child sits 1.3 m from the center and the other sits 1.2 m and weighs 45 kg. Determine the weight of the other child.
41.5 kg
A race car travels in a circular track of radius 200 m. If the car moves with a constant speed of 80 m/s, find its angular velocity.
0.4 rad/s
An old phonograph played a record at 4.71 rad/sec then the motor is turned off, taking 0.75 seconds to come to a stop. Determine the angular acceleration.
- 6.28 rad/s2
0.15 kg meter stick is balanced with the pivot point at the 18 cm mark. A weight of 3.2 N is hung from the shorter end. Where the weight should be positioned in order to balance the meter stick?
0.15 m
A soccer ball has a mass of 0.45 kg and a radius of 11 cm. Determine the soccer ball's moment of inertia.
0.002 kgm2
A solid steel wheel is free to rotate about a motionless central axis. It has a mass of 15 kg and a diameter of 0.5 m and starts at rest. You want to increase this wheel’s rotation about its central axis to 11.5 rev/s in 10 s. If you apply the torque by wrapping a strap around the outside of the wheel, determine how much force should you exert on the strap.
13.56 N
A golfer applies 50 Nm of torque to his golf club. Assuming the club is a 1 m long rod, with a mass of 0.5 kg being pivoted at its end, determine the moment of inertia of the golf club.
0.32 kgm2
A 0.5-meter diameter bicycle wheel is rotating at 60 revolutions per minute. What is its initial angular speed in radians per second?
6.28 or 2π rad/s
A child (41 kg) and her younger (29 kg) want to balance on a 3.1 m long seesaw. Where should they place the pivot point of the seesaw?
1.82 m from the younger sister and 1.28 m from the other child
A drumstick has a mass of 60 g and a length of 0.4 m. Determine the moment of inertia if the drumstick has an axis of rotation through the center.
0.008 kgm2
The solid sphere has a mass of 5.2 kg and a diameter of 0.55 m. It is at rest, and you need it to rotate at 12 rev/s in 35 s. If a nylon strap is wrapped around the outside of the sphere, determine how much force do you need to exert on the strap.
1.23 N
A figure skater begins spinning counterclockwise at an angular speed of 4.0π rad/s. During a 3.0 sec interval, she slowly pulls her arms inward and finally spins at 8.0π rad/s. Determine her average angular acceleration during this time interval and many rotations did she spin in this time interval.
4.2 rads/s2 and 9 rotations