Exercises: Rotational Kinematics
A bicycle wheel turns through $12$ complete revolutions as Emma rides down her street. Express the wheel's angular displacement in radians. Give your answer in terms of…
A bicycle wheel turns through $12$ complete revolutions as Emma rides down her street. Express the wheel's angular displacement in radians. Give your answer in terms of $\pi$ and also as a decimal number.
A vinyl record on a turntable rotates at a constant $33\tfrac{1}{3}$ revolutions per minute. Convert this rate to an angular velocity in rad/s, and then find the time…
A vinyl record on a turntable rotates at a constant $33\tfrac{1}{3}$ revolutions per minute. Convert this rate to an angular velocity in rad/s, and then find the time the record takes to complete one revolution.
A point on the rim of a merry-go-round at a park in Denver is $2.0$ m from the center. The merry-go-round rotates with a constant angular velocity of $1.5$ rad/s. Find…
A point on the rim of a merry-go-round at a park in Denver is $2.0$ m from the center. The merry-go-round rotates with a constant angular velocity of $1.5$ rad/s. Find the linear speed of this point.
A ceiling fan starts from rest and speeds up with a constant angular acceleration of $0.80$ rad/s$^2$ for $10$ s. (a) Find the fan's angular velocity at $t = 10$ s. (b)…
A ceiling fan starts from rest and speeds up with a constant angular acceleration of $0.80$ rad/s$^2$ for $10$ s. (a) Find the fan's angular velocity at $t = 10$ s. (b) Find the angular displacement during these $10$ s. (c) Find how many revolutions the fan makes in that time.
Marcus's car tire has a radius of $0.32$ m. The car speeds up from rest to $20$ m/s in $8.0$ s on a straight road, and the tires roll without slipping. Assuming constant…
Marcus's car tire has a radius of $0.32$ m. The car speeds up from rest to $20$ m/s in $8.0$ s on a straight road, and the tires roll without slipping. Assuming constant acceleration, find (a) the tire's angular acceleration and (b) the tire's angular velocity at $t = 8.0$ s.
A grinding wheel spinning at $60$ rad/s is switched off and slows uniformly to rest in $15$ s. (a) Find the magnitude of its angular acceleration. (b) Find the angular…
A grinding wheel spinning at $60$ rad/s is switched off and slows uniformly to rest in $15$ s. (a) Find the magnitude of its angular acceleration. (b) Find the angular displacement while it slows. (c) A point on the wheel is $0.10$ m from the axis. Find the tangential acceleration of that point.
A clothes dryer drum of radius $0.30$ m starts from rest and has a constant angular acceleration of $2.0$ rad/s$^2$. A sock sits against the inside wall of the drum and…
A clothes dryer drum of radius $0.30$ m starts from rest and has a constant angular acceleration of $2.0$ rad/s$^2$. A sock sits against the inside wall of the drum and moves with it. At $t = 3.0$ s, find (a) the sock's tangential acceleration, (b) its centripetal acceleration, and (c) the magnitude of its total acceleration. (d) Explain why the angle between the total acceleration vector and the radial direction changes as time passes, and say whether it increases or decreases.
Two students study a spinning disk. The disk's angular velocity is given in the table below. | $t$ (s) | 0 | 2.0 | 4.0 | 6.0 | 8.0 | |---|---|---|---|---|---| | $\omega$…
Two students study a spinning disk. The disk's angular velocity is given in the table below.
| $t$ (s) | 0 | 2.0 | 4.0 | 6.0 | 8.0 |
|---|---|---|---|---|---|
| $\omega$ (rad/s) | 4.0 | 10.0 | 16.0 | 22.0 | 28.0 |
(a) Show that the angular acceleration is constant and find its value. (b) Find the angular displacement from $t = 0$ to $t = 8.0$ s. (c) Aaliyah says the disk makes about $22$ revolutions in this interval. Check whether she is correct, and explain your reasoning with a calculation.