Free Printable WorksheetScienceGrade 12Science Curriculum12.77

12.77 Rotational Dynamics Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Physics Science worksheet provides structured practice on 12.77 Rotational Dynamics. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Rotational Dynamics: Determine angular acceleration or net torque using rotational analogs of Newton's laws. Aligned to NGSS, CCSS Literacy and Mathematics, AP Physics, and selected state frameworks 12.77 - Rotational Dynamics: NGSS HS-PS2-1/2/3; HS-ETS1 engineering connections; CCSS HSN-Q.A, HSA-CED.A, HSG-MG; AP Physics 1 Units 5-6; AP Physics C: Mechanics rotation enrichment; TX TEKS Physics §112.45(c); FL SC.912.P.12; VA PH.4; MA/CA/NY HS-PS2/ETS1.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Physics

Subject

Science

Domain

Science Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 12.77 Rotational Dynamics skill assessments:

Problem 1Difficulty: Mastery

A flywheel has I = 3.0 kg*m². A 2.0 kg ring of radius 0.50 m is attached to it, so the ring rotates with the flywheel. The system must slow from 30 rad/s to 10 rad/s in 5.0 s. Bearing friction already provides a -2.0 N*m torque. What additional braking torque magnitude is required?

A14 N*m

B8 N*m

C16 N*m

D12 N*m

Solution & Explanation:The ring adds I = MR² = (2.0)(0.50)² = 0.50 kg*m², so I_total = 3.50 kg*m². The angular acceleration is (10 - 30)/5.0 = -4.0 rad/s². Required net torque is (3.50)(-4.0) = -14 N*m. Bearing friction supplies -2.0 N*m, so the additional brake must supply -12 N*m, magnitude 12 N*m.

Problem 2Difficulty: Mastery

A 60 N force is applied at the rim of a disk at radius 0.30 m, but only 45 N of the force is tangential in the positive direction. Rotational drag provides -4.5 N*m. If I = 0.90 kg*m², what is the angular acceleration?

A+15 rad/s²

B+5.0 rad/s²

C+10 rad/s²

D+20 rad/s²

Solution & Explanation:Only the tangential component produces torque: tau_applied = (0.30)(45) = 13.5 N*m. Net torque = 13.5 - 4.5 = 9.0 N*m. Then alpha = 9.0/0.90 = +10 rad/s².

Problem 3Difficulty: Mastery

A uniform 2.0 m beam of mass 6.0 kg rotates about its center, so I = (1/12)ML². An upward 20 N force acts at the right end, and an upward 10 N force acts at the left end. A friction torque opposes the positive rotation. If the desired angular acceleration is +4.0 rad/s², what friction torque magnitude is required?

A8.0 N*m

B2.0 N*m

C10 N*m

D18 N*m

Solution & Explanation:The beam's rotational inertia is (1/12)(6.0)(2.0)² = 2.0 kg*m², so the desired net torque is (2.0)(4.0) = +8.0 N*m. The right upward force gives +20 N*m, while the left upward force gives -10 N*m, for +10 N*m before friction. Friction must reduce this to +8 N*m, so its magnitude is 2.0 N*m.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Physics Science students. It aligns with educational standard 12.77 (NGSS HS-PS2-1/2/3; HS-ETS1 engineering connections; CCSS HSN-Q.A, HSA-CED.A, HSG-MG; AP Physics 1 Units 5-6; AP Physics C: Mechanics rotation enrichment; TX TEKS Physics §112.45(c); FL SC.912.P.12; VA PH.4; MA/CA/NY HS-PS2/ETS1.).