Rotational Dynamics

When would a force applied to a rigid body lead to zero torque?

• When the force is directed towards or away from the axis of rotation.

• When the force is applied perpendicular to the lever arm

• When the force is a gravitational force

• When the force is a normal force

Answer explanation

Forces towards or away from the AoR make an angle of 0 degrees with the lever arm, and therefore do not exert torques on systems.

Think: can you spin a bike wheel by pushing towards the center of the wheel?

If an object is moving in a circle of radius r with a constant speed v, what is its angular velocity?

Hint: v = rω

• v² / r

• vr

• v / r

• r / v

A disk rotates with an angular speed (ω). What is the magnitude of the tangential velocity (v) of a point on the disk located a distance (r) away from the axis of rotation?

Hint: Check your notes from Week 22. Go to the section titled, "Angular Speed and Tangential Speed."

What is Klyde's angular velocity?

• The same as Bonnie's

• Twice Bonnie's

• Half of Bonnie's

• 1/4 Bonnie's

Answer explanation

Angular speed is the same for all points on a rotating rigid body.

What is happening to the ice skater as she brings her leg closer to her torso?

Hint: α = τ / I

and

I = Σm_ir_i²

• Decreased angular velocity, decreased moment of inertia

• Decreased angular velocity, increased moment of inertia

• Increased angular velocity, increased moment of inertia

• Increased angular velocity, decreased moment of inertia

Answer explanation

Net external torque is 0Nm on the skater, so L is conserved.

Since L is Iw, as I decreases, w must increase so L remains constant.

The graph above shows the angular velocity (ω) of an object with respect to time.

During which time intervals is there a net torque (τ_net) on the object? Select all that apply.

• 0-2s

• 2-6s

• 6-8s

• 8-10s

Answer explanation

Net torques will cause angular accelerations.

Angular acceleration is the slope of a w vs. t graph.

What is Klyde's tangential velocity (v)?

Hint: v = rω

• The same as Bonnie's

• Twice Bonnie's

• Half of Bonnie's

• 1/4 Bonnie's

Answer explanation

While w is constant on all points of a rotating rigid object, v changes with r according to the equation: v=wr.

A force (F) is applied to a wrench to turn a bolt. The moment of inertia (I) is given for the different bolts.

Which of the following bolts has the greatest angular acceleration (α)?

Hint: α = τ / I = F_⟂r / I

• F

• A

• B

• E

• C

Answer explanation

Angular acceleration is equal to net torque/rotational inertia.

A force (F) is applied to a wrench to turn a bolt. The moment of inertia is given for each bolt.

Which of the following bolts has the greatest torque? Select all that apply.

Hint: τ = F_⟂r

• E

• B

• C

• D

• F

Answer explanation

Torque is Frsin(angle).

Torque is maximum when the angle between F and r is 90.

Does this result make sense? If yes then why? if no, then Why not?