Unit 5 check

Unit 5 check: Torque and Rotational Dynamics

10 questions from 6 lessons in Unit 5. Answer each one, and if you miss, follow the link back to where it is taught, then try again. Your score counts first tries.

Question 1 · from 5.1 · Fill the statement

A bicycle sits upside down on a repair stand. Take counterclockwise, as seen from the chain side, as positive. A mechanic turns the front wheel through 3 full revolutions, clockwise as seen from the chain side.

The wheel is modeled as a . Its angular displacement is , and a spot on the rim and a spot near the hub turn through .

Question 2 · from 5.2 · Spot the error

A grinding wheel speeds up with angular velocity $ω (t) = t^{3}$ , with $ω$ in rad/s and $t$ in seconds; counterclockwise, as seen from the front, is positive. A student finds the tangential acceleration of a point on the rim, 0.10 m from the axis, at $t = 2.0$ s. Tap the first line with a mistake.

Question 3 · from 5.3 · Decide and justify

A driver holds a steering wheel of radius 0.18 m at the 9 o'clock and 3 o'clock positions. Her left hand pulls down on the rim with 30 N, and her right hand pushes up on the rim with 30 N. Seen from the driver's seat, take counterclockwise as positive. A classmate draws a free-body diagram with both forces on one dot, sees that they add to zero, and says the hands exert no net torque on the wheel about its axle. Is the classmate right?

Which reason supports your answer?

Question 4 · from 5.4 · Decide and justify

A light rod 0.90 m long has a 2.0 kg ball at its left end and a 1.0 kg ball at its right end; treat each ball as a point. The rod can be spun about any axis that crosses it at a right angle. About which of these axes is the rotational inertia least?

Which reason supports your answer?

Setup for question 5

On paper. A uniform shelf board 1.2 m long and weighing 30 N is screwed to two brackets, one 0.2 m from each end, and a 50 N stack of books sits at the board's right end. Draw a force diagram of the board, with each force starting at the point where it is exerted, and label each force's lever arm about the left bracket. Then write the torque sum about the left bracket with counterclockwise positive, seen from the front, and set it to zero. You do not need to solve it. There is nothing to submit here. To compare: measured from the left bracket, the left bracket's force is at 0, the board's 30 N weight at 0.4 m, the right bracket's force at 0.8 m and the books' 50 N at 1.0 m, and the sum is $F_{R} (0.8) - (30) (0.4) - (50) (1.0) = 0$ .

Question 5 · from 5.5 · Calculate

A flywheel turns counterclockwise as seen from above, and keeps turning counterclockwise for the whole time described; counterclockwise is positive. Its motor exerts a torque $τ_{m} (t) = 6.0 - 2.0 t$ , with $τ_{m}$ in N·m and $t$ in seconds, for $0 \leq t \leq 5.0$ s (a negative value means the motor brakes). Friction at the axle exerts a steady torque of 2.0 N·m clockwise. At what time is the flywheel's angular velocity greatest?

Your answer s

Setup for question 6

A class measures a turntable's rotation. A string wrapped around the turntable's hub, of radius 0.050 m, is pulled tangentially by a force sensor that holds the tension steady, and a rotary motion sensor records the angular acceleration. Counterclockwise as seen from above is positive. Friction at the axle is the same in every trial.

Turntable trials, string on the 0.050 m hub
Tension $T$ (N)	Angular acceleration $α$ (rad/s²)
1.0	3.0
2.0	8.0
3.0	13.0
4.0	18.0

Question 6 · from 5.6 · Calculate

Using the data, what is the turntable's rotational inertia? Counterclockwise as seen from above is positive.

Your answer kg·m²

Question 7 · from 5.1 · Calculate

A drill bit's angular position is $θ (t) = 0.5 t^{3} + 3 t$ , with $θ$ in radians and $t$ in seconds. Take counterclockwise, as seen from behind the drill, as positive. What is the bit's angular acceleration at $t = 2.0$ s?

Your answer rad/s²

Setup for question 8

On paper. Draw the chainring and the rear sprocket as two circles joined by the chain, and mark the chain speed $v$ at the top of each. Then derive, in symbols, the speed of the rear tire's edge in terms of the chainring's angular velocity $ω_{c}$ , the chainring radius $r_{c}$ , the sprocket radius $r_{s}$ and the wheel radius $R$ . Then substitute the trainer question's numbers into your expression and check that it gives the same speed you found there. There is nothing to submit here; compare your expression with the chain of steps in that question's explanation.

Question 8 · from 5.2 · Rank it

A bicycle chain runs without slipping around a front chainring of radius 0.10 m and a rear sprocket of radius 0.040 m. The rear wheel is rigidly fixed to the rear sprocket and turns with it. While the rider pedals, rank the three by the magnitude of angular velocity.

Greatest first

Give each one a place, 1 for first. Give two the same place if they are equal.

Front chainring
Rear sprocket
Rear wheel

Your ranking: none yet

Question 9 · from 5.3 · Fill the statement

A 0.30 m wrench points straight to the right from the center of a bolt, and you push straight up on its end with a 50 N force. You look at the wrench from the front.

Here $\vec{τ} = \vec{r} \times \vec{F}$ has size . It points along the bolt's axis, to the plane that holds $\vec{r}$ and $\vec{F}$ , and seen from the front your push tends to turn the bolt .

Setup for question 10

On paper. Draw the disk hanging from the nail in the question above. Mark its center of mass, the nail, and the distance $d$ between the two parallel axes, labeled with its value. Then, beside it, sketch a graph of the disk's rotational inertia against $d$ as the nail hole is moved from the center out to the rim, $d = 0$ to $d = 0.25$ m, and label the value at $d = 0$ . There is nothing to submit here. Your graph should start at its lowest value at $d = 0$ and curve upward like the rod graph at the top of the page, since the shift term grows as $d^{2}$ .

Question 10 · from 5.4 · Sort it

Tap a card, then say what happens to the rotational inertia about the axis named on the card.

Increases

Decreases

Stays the same

0 of 10 answered.